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wraa R.R.3 



R 



THE OPUS MAJUS 

OF 

ROGER BACON 



VOL. I. 



^ 



HENRY FROWDE, M.A. 

PUBLI8HBR TO THB UMIVBRSITY OF OXPORD 




LONDON, RDINBURGH AND N£W YORK 



THE 

'OPUS MAJUS' 

OF 

ROGER BACON 

EDITBD, WITH 

INTRODUCTION AND ANALYTICAL TABLE 

BV 

JOHN HENRY BRIDGES 

FBLLOW OF THE ROYAL COLLfcGK OF PHV^n lANS 
SOlfBTIlfB FBLLOW OF ORr^L COLLEGE 



* Induire pour dtiuirc afin dt cofLftruLre ' 

AuGUSTE Cqutk 

* OmiMt icknri— fOBt ooimexae, et matuLs &e fovent «uilik, »cat pnrtes ejuideai 
totiQS, qnanun qnaelibet opa» soum perag ii non sobni pro ie sed pro lUUs ' 

RoGER Bacon, C/«* Ttrtinm 



VOLUME I 



WILLIAMS AND NORGATE 

14 HENRIETTA STREET, COTONT GARDEN, LOXCJON 

ao SOUTH FREDERICK STREET, EDtNBURGH 

AND 7 BROAD STREET, OXFORD 

1900 



/ 



t 

C 

t 



COLLEGIO REGALI MEDICORUM LONDINENSI 

CUJUS OLIM PRAESIDENS 

RICARDUS MEAD 

LITTEiaS PKRINDE AC SCIJENTIIS ILLUSTRIS 

PRIXUM BACONIS KDITORKM CONSILIIS INSTIGAVIT JUVIT 

ALTERAM KDITIONEM DKDICO 



PREFACE 



A suFFiciENT reason for a new edition of Roger 
Bacon's principal work would be the extreme rarity of 
the edition of the Opus Majus published by Jebb in 
1733, and reprinted seventeen years afterwards in 
Venice. But a more cogent reason is that this edition 
is incomplete. The work, as we learn from Bacon's 
account of it in his Opus Tertiuniy consisted of seven 
parts; and the seventh part, a discourse on Moral 
Philosophy, was omitted by the editor. 

Why Jebb should have taken this course is not 
clear. In his preface he speaks of the work as con- 
sisting of six parts, * in sex partes distributum/ and adds, 
* tractatum de Morali Philosophia ad calcem adjunxit.' 
In 1858 a paper was read by Dr. Ingram before the 
Royal Irish Acadeoiy, and was printed in the seventh 
volume of the Proceedings of this institution, in which 
the writer showed conclusively the continuity of this 
seventh part of the Opus Majus with all that had gone 
before. The continuity is marked unmistakably in 
the very title of the section, Ifuipit septima pars hujus 
persuasionis de Morali Philosophia, and in its opening 
words, * Manifestavi in praecedentibus,' &c. Repeated 
references to the foregoing parts will be found ; and if 



viii PREFACE. 

further proof were wanting, it is supplied in abundance 
by the two appendages to the Opus Majus which were 
sent by Bacon to Pope Clement IV within a few 
months of the dispatch of the principal work, published 
by Professor Brewer in 1859, in the Rolls Series, as 
Opera Inedita. Special mention is made in the Opus 
Minus (Brewer, p. 315) of passages of this seventh 
section which the author regarded as of special im- 
portance. In the Opus Tertium (Brewer, pp. 48-52), 
a brief account is given of each of the six divisions of 
which it consisted. 

Dr. Ingram*s paper was carefuUy studied by Victor 
Cousin, who had already devoted much time to the 
study of Bacons unpubUshed works. He remarked 
upon it {Journal des Savants, 1859, p. 717), * Nous 
croyons qu'il n'y a pas d exemple dans Thistoire litt6- 
raire d*une erreur semblable a celle de Jebb. Elle 
est vraiment 6tonnante, mais elle est incontestable/ 
And in truth the omission is of much greater signifi- 
cance than the mere loss of Bacons opinions on a 
subject of importance would imply. Throughout the 
Opus Majus there is an orderly arrangement of the 
subject-matter formed with a definite purpose, and 
leading up to a central theme, the consolidation of the 
Catholic faith as the supreme agency for the civiliza- 
tion and ennoblement of mankind. For this end 
a complete renovation and reorganization of man s 
intellectual forces was needed. After a brief exposition 
of the four principal impediments to wisdom — autho- 
rity, habit, prejudice, and false conceit of knowledge — 
Bacon proceeds in his second part to explain the 
inseparable connexion of philosophy with the highest 
truths of religion. In primaeval ages both were 
entrusted to the patriarchs. Subsequently, while the 



PREFACE. ix 

eyolution of religious truth was proceeding in Judaea, 
Greece became the scene of the growth of philosophy. 
Both were alike ordained in God's providence. In our 
own times, as in those of antiquity, the study of both 
should be carried on continuously. But for this 
purpose it was essential that the wisdom of the ancients 
should be studied in the language in which it was 
originally set forth. To limit students to Latin trans- 
lations is to ensure the multiplication of error. Most 
of these translations, especially those of the Bible and 
of Aristotle, are deplorably defective, and have been 
made by men imperfectly acquainted with the subject 
treated of The first condition, therefore, of a renova- 
tion of learning is the systematic study of at least three 
lang^ages besides Latin, namely, Hebrew, Greek, and 
Arabic. 

The second condition was the application of mathe- 
matical method to all objects of study, whether in the 
world or in the Church. Mathematic is the * gateway 
and the key to all other sciences ' ; it raises the under- 
standing to the plane at which knowledge can be 
distinguished from ignorance. Without it other sciences 
are unintelligible. It reveals to us the motions of the 
heavenly bodies, and the laws of the propagation of 
force in things terrestrial, of which the propagation of 
light may be taken as a type ; without it we are 
incapable of regulating the festivals of the Church ; 
we remain in ig^orance of the influences of cHmate 
upon character ; of the position of cities and of the 
boundaries of nations whom it is the function of the 
Catholic Church to bring within her pale, and to control 
spiritually. With these subjects the fourth and fifth 
scctions of the Opus Majus are occupied ; they form 
the principal bulk of its contents. But mathematical 



X PREFACE, 

method, though essential, is insufficient It must be 
supplemented by the method of experiment Even 
a purely geometrical proof is not convincing or con- 
clusive, until the execution of the diagram has enabled 
us to add ocular, that is to say, experimental, evidence 
that the demonstration is sound. This method, 
moreover, will lead us into new regions into which 
mathematical procedure is not able to penetrate. 
Experimental science governs all the preceding sciences 
(* domina est omnium scientiarum praecedentium '), it 
controls their methods ; in prosecuting its own special 
researches it makes use of their results. 

Here then ends the Opus Majus as presented in the 
edition of 1733- A glance at the fourteenth and pre- 
ceding chapters of the Opus Tertium, in which the 
structure and purpose of the Opus Majus are reviewed, 
will show how disastrously the suppression of the 
seventh section of the work has mutilated it * AU 
these foregoing sciences,' says Bacon, *are, properly 
speaking, speculative. There is indeed in every 
science a practical side, as Avicenna teaches in the 
first book of his Art of Medicine. Nevertheless, of 
Moral Philosophy alone can it be said that it is in the 
special and autonomatic sense practical, dealing as it 
does with human conduct with reference to virtue and 
vice, beatitude and misery. All other sciences are 
called speculative : they are not concerned with the 
deeds of the present or future life affecting man*s 
salvation or damnation. AU procedures of art and of 
nature are directed to these moral actions, and exist on 
account of them. They are of no account except in 
that they help forward right action. Thus practical 
and operative sciences, as experimental alchemy and 
the rest, are regarded as speculative in reference to the 



■^^ 



PREFACE. SJ 

operations with which moral or political science is con- 
cerned. This science is the mistress of every depart- 
ment of philosophy. It employs and controls them 
for the advantage of states and kingdoms. It directs 
the choice of men who are to study in sciences and 
arts for the common good. It orders all members of 
the state or kingdom so that none shall remain without 
his proper work.' 

The seventh part of the Opus Majus is for the first 
time printed in this edition. Unfortunately it is not 
complete. It consisted, as we learn from the fourteenth 
chapter of the Opus Tertium^ of six divisions ; and the 
only two MSS. of it as yet discovered, those of Dublin 
and Oxford (the first of which, as will be shown after* 
wards, is copied from the second), stop short before the 
conclusion of the fourth. We gather, however, that 
the missing portions are not of primary importance. 

Another alteration of considerable importance has 
been made in the present edition. Professor Emile 
Charles, in his very important monograph on Roger 
Bacon (Bordeaux, 1861), pointed out that the treatise 
De Multiplicatione Specierum, which in Jebbs edition 
of the Opus Majus is placed between the fifth and 
sixth sections of the work, does not in reality belong 
to it. And indeed the second sentence of the treatise 
makes this evident. * Recolendum est,' Bacon observes, 
'quod in tertia parte hujus operis tactum est quod 
essentia, substantia, natura, potestas, potentia, virtus, 
vis, significant eandem rem.' No such passage is to 
be found in any part of the Opus Majus, least of all in 
the third part, which deals with Comparative Philology, 
Here again the Opus Tertium comes to our aid. Several 
references will be found there to a distinct treatise 
sent to Pope Clement IV simultaneously with the Opus 



xii PREFACE, 

Majus (Brewer, pp. 38, 99, 117, 227). It is a treatise 
on the propagation of radiant forces, usually spoken of 
as Multiplicatio Specierum, but in one passage entitled 
Tractatus de Radiis, quem vobis misi separatim ab 
Opere Majori. In the present edition this treatise 
will be found in its proper place as an appendix to the 
Opus Majus. 

It must be added that the text, as edited, is in 
certain parts of the work far from perfect. This 
remark applies especially to the third and sixth sections. 
In the third section several missing pages have been 
supplied from a Cottonian MS. (Julius D.v.), con- 
taining amongst other things a Greek and a Hebrew 
alphabet It is the more remarkable that Jebb should 
have omitted these passages, since it is clear that he 
had consulted this MS. and had made frequent correc- 
tions from it. The sixth section, on Experimental 
Science, has been so carelessly edited that it seems 
probable that the editor must have entrusted the 
work to a less competent assistant. Contractions of 
the most ordinary kind are misinterpreted (as e.g. 

* e converso ' is rendered * ergo,* * conclusio * is written 

* quaestio,' &c.), and in some passages sentences have 
been omitted. While indicating these shortcomings, 
it ought at the same time to be added that other 
parts of the work give proof of great labour and care 
in the coUation of the MSS. consulted. This is 
especially the case with the fourth and fifth parts, 
which form a very large proportion of the whole work. 
Having spent much time over the MSS. used by Jebb, 
in addition to others, I can bear testimony to the 
accuracy with which variations have here been noted. 
AII of them which are of more than verbal importance 
have been noted in the present edition. 



■ep 



X" 



PREFACE. xiii 

A further change has been made m ihe arrangement 
of the diagrams, which in Jebb's edition were collected 
into two tables, and thus rendered inconvenient for 
comparison with the text, and which, nioreover, in 
many cases are incorrectly drawn. They have been 
carefully re-copied from a MS. in the British Museum 
(Royal, 7 F. viii), which Sir E. Maunde Thompson, 
who was so kind as to examine this and several other 
Baconian MSS. in the British Museum for me, pro- 
nounces to be of the latter part of the thirteenth 
century, i.e. contemporary, or very nearly so; with 
Bacon. Each diagram has been placed in its proper 
context. 

It was found that in many cases the reasoning of 
the author had been entirely nuUihed by defective 
punctuation. This has been entirely rcvised, and the 
number of distinct sentences and paragraphs has been 
very largely increased. Students of t!ie Ofi?is J/ajns 
have found the work difficult to refer to, owing to the 
multipHcity and diversity of the subjccts treated, and the 
want of such guidance as page-headings or marginal 
notes can supply. This defect has been remedied, an 
analysis of the work hasbeen prefixed, and an improved 
index added. 

A few remarks on the MSS. of ihe Opus Majus. 
Jebbs edition was founded on a MS. in the library of 
Trinity CoUege, DubHn, which at that time was the 
only MS. known to contain the complete work. It con- 
tains a note in Archbishop Usher s handwriting to the 
effect that the MS. was presented to the Collcge by 
Gordian Strowbridge, and that thc diagrams wcre 
drawn by Sir Christopher Heyden. This MS. is very 
clearly written in 249 folios of four columns. Sir 
Christopher Heyden, of Baconsthorpe, in Norfolk, was 



xiv PREFACE. 

a well-known astrological writer who died in 1623, 
which fixes the date of this MS. at the end of the 
sixteenth or beginning of the seventeenth century. 
A glance at the MS. shows that the figures were 
drawn simultaneously with the text, room being left 
in each page for their insertion. The character of the 
writing quite correspohds with this date. It is referred 
to in this edition as D. 

In 1825 another MS. of the Opus Majus was 
bought for the Bodleian Library. It belonged at one 
time to Thomas Allen, the astrologer of Gloucester 
Hall, who early in the seventeenth century gave twenty 
MSS. to the Bodleian. This one, however, passed 
into the possession of Sir Kenelm Digby, whose well- 
known signature and motto are inscribed on the first 
page. It is now numbered 235 of the Digby MSS. 
The greater part of it is of the fifteenth century. 
But a portion of it (pp. 249-295) is in an older and 
more beautiful handwriting, considered by Mr. Coxe 
to be of the fourteenth century. This portion in- 
cludes a considerable portion of the Perspectiva, 

These two MSS. have been carefully collated for 
the present edition. In the course of the collation 
unmistakable proof was given that the Dublin MS. 
was a copy of that in the Bodleian. At the close of 
p. 470, col. 2, of this latter, the sentence breaks ofF 
midway, and is continued on the first line of p. 487, 
col. I. An error of this kind, analogous to that caused 
by the transposition of sheets in binding a modern 
book, is easily explicable. In the Dublin MS. the 
same rupture of the sentence occurs, but in the middle 
of a column (fol. 224, col. a, line 12), the sentence 
being ultimately continued on fol. 229, col. d, line 14. 
It may be added that these two MSS. exhibit through- 



PREFACE. XV 

out an almost exact correspondence in their errors and 
in their variants. The Oxford MS. has therefore been 
taken as the foundation of the present edition, and 
is denoted by the letter O, It is, however, by no 
means perfect, especially in the second and third 
sections of the work : and recourse was had both by 
Jebb and by the present editor to various MSS. in 
the British Museum and elsewhere to supply the 
imperfections. Foremost among these are the two 
Cottonian MSS., Julius D.v., and Tiberius C.v. (desig- 
nated here as Jul. and Tib.). The first of these, 
unfortunately much injured in the fire of 1731, gives 
the first three sections of the work and a large part of 
the fourth. The second gives the whole of the fourth. 

For the geographical portion of the fourth section, 
I was allowed to consult the MS. in the possession of 
Corpus Christi CoUege, Cambridge. It is not, how- 
ever, believed to be of earlier date than the middle or 
later part of the fifteenth century. Occasional reference 
has been made to a MS. of the fifth section of the work 
{Perspectiva) in the possession of Magdalene CoUege, 
Cambridge, which I was permitted to examine. It is 
not, however, of earlier date than the Bodleian MS., 
and its variants are not of great importance. 

Of the MSS. of the Perspectiva and of the De 
Multiplicatione Specierum which appear to have been 
transcribed more frequently than other portions of the 
work, by far the most important is the British Museum 
MS. (Royal, 7 F. viii), already spoken of as contem- 
porary, or nearly so, with Bacon. This, as I have said, 
was carefuUy coUated by Jebb, who indeed has in 
certain places copied on the margin extracts from 
Combach's printed edition of the Perspectiva of 16 14. 
The diagrams of this MS. are of special value. The 



XVI FREFACE. 

Sloane MS. 2156, and the Harleian MS. 80, 60 b, 
have also been consulted. 

The sixth section of the Opus Majus {Scientia 
Experinientalis) appears to have been seldom copied. 
In the third volume of Baconian MSS. presented to 
University CoUege, Oxford, by John Elmhurst, there 
is a MS. of this section which is described as copied 
from Allens MSS. (see Brewer, p. xliii). It may, 
therefore, be merely copied from the Oxford MS. of 
the Opus Majus. But it offers some variants, and in 
one or two passages it has proved serviceable. It is 
spoken of in this edition as U. 

Of the seventh section, here printed for the first 
time, there is a MS. in the Royal Library (8, F. ii) 
containing the first two parts and a portion of the 
third. This has been carefully coUated with the 
corresponding parts of the Dublin and Oxford MSS. 
The variations will be seen to be of no great impor- 
tance. The MS. appears to be of the middle of the 
fifteenth century. 

Besides these MSS., others have been consulted 
which throw light on Bacons Hfe and work. Chief 
amongst these is the important MS. of the Mazarin 
library (formerly numbered 1271, but at present 3576), 
from which Professor Emile Charles gives copious ex- 
tracts in his monograph entitled Roger Bacon, sa vie, ses 
ouvrages, ses doctrineSy cCapres des textes inddits (Bor- 
deaux, 1861). More will be said afterwards of its 
contents. They offer a considerable instalment of 
the Scriptum Prificipale^ of which the Opus Majus, 
inclusive of its adjuncts, the Opus Minus and the 
Opus Tertium, was but the prelude. 

Another valuable fragment of this linal work is 
preserved in the British Museum among the Sloane 



PREFACE. xvti 

MSS. (2156). It contains the lirst book and part of 
the second of the Commiinia Matkematicae, Attention 
was called to it both by Brewer and by Charles, and 
occasional references to it have been made in the 
present edition. 

Yet a third fragment is the elementary work on 
Greetc grammar in the possession of Corpus Christi 
College, Oxford, which was sent to the Bodleian for 
my perusal. An imperfect copy, in seventeenth cen- 
tury handwriting, apparently made from the Corpus 
MS., is contained among the Baconian MSS. of 
University CoUege. 

Bacon*s commentary on the Secretum Secretorum 
(Tanner MSS. 116) has also been examined. It throws 
light on the astrological side of his work. 

Among the books consulted for this edition, far the 
most important are those of Professors Brewer and 
]£mile Charles, already spoken of. It is unfortunate that 
two such assiduous and able investigators should have 
worked simultaneously and without communication. 
Several not unimportant errors might have been 
avoided, had either of them known of the others 
work. Charles had a far more extensive knowledge 
than Brewer of Bacons unpubhshed works; and his 
extracts from them are so copious as to render it 
desirable that his monograph, which has already 
become extremely rare, should be republished. He 
makes, however, the erroneous statement (p. 62) that 
the missing portion of the Opus Majus (here printed 
for the first time) had been published in Dublin ; and 
he does not appreciate the distinction, so clearly 
demonstrated by Professor Brewer, between the Opus 
Tertium (which is at once an introduction and a supple- 
ment to the Opus Majus), and the far vaster Scriptum 

VOL. I. b 



xviii PREFACE. 

Principale projected by Bacon, but only in part 
executed. On these points, and on the bibliography 
of Bacon generally, Mr. Little s Grey Friars in Oxford 
is of great value. Other works consulted will be 
noted as reference is made to them. Attention, how- 
ever, may be specially called to Govi's recent edition 
of the Latin translation of Ptolemy s Optica, so fre- 
quently used by Bacon (Turin, 1885), a publication 
of the greatest value for the history of science ; and 
to Heibergs edition of Euclids Optica (vol. vii. of 
his edition of Euch'd, Leipsic, 1895). Wuestenfelds 
Geschichte der Aradischen Aerzte (Gottingen, 1840), 
and Cantor s Geschichte der Mathematik (Leipsic, 1880- 
1892), throw light on the mediaeval men of science, 
Eastern or Western, mentioned by Bacon. Haur6au*s 
Histoire de la Philosophie Scolastiqtie (Paris, 1872) 
defines, with some acerbity, Bacons position among 
the schoolmen. Jourdain's Recherc/ies critiques sur 
les traductions latines d^Aristate (nouvelle 6dit,, 1843) 
contain indispensable information as to the translators 
of whose shortcomings Bacon so often complains. 

F^or the geographical section of the work, in addition 
to the classical works of Yule and Bunbury, frequent 
reference is made to the complete version of the travels 
of Rubruquis and Carpini, published by the Paris 
Geographical Society, in ihe fourth volume of their 
Recueil de Voyages et de M^moires (1839). 

As Seneca occupies so large a place in the seventh 
section of the Opus Majus^ it may be mentioned that 
the edition used for this work is that of Haase (Leipsic, 
1887). As to Aristotle, the references are to Didots 
edition (Paris, 1848-1873). 

It remains for me to express my thanks to the 
Master and Fellows of Trinity CoUege, Cambridge ; to 



PREFACE. XIX 

the Master and Fellows of Corpus Christi CoUege, 
Cambridge; the Master and Fellows of Magdalene 
CoUege, Cambridge ; and the President and Fellows 
of Corpus Christi College, Oxford, for permission to 
examine the MSS. of Bacon belonging respectively 
to these societies. 

J. H. B. 

March 26, 1897. 



ba 



FACTS RELATING TO BACONS LIFE 



CoHlimporary Evont». 



1200. Condemnation of 

AriiitoCle'f Physic and 

Metaph^rsic in Paris. 
1215. Confirmation of thit 

hy Papal Legate. (Cp. 

Opu» itrHum^ cap. 9. ■ 
1999. Alexander of Hales 

enten the Franciscan 

Order, and teaches phi- 

lofophy in Paris. 
1281. Condemnation of 

Phynic and Metaphyaic 

partially removed by 

Gregory IX. 
1988. Alfxander of Halef 

resiKnf his post as a 

tcachcr of philosophy. 
1946--8. First residence of 

Thomas Aquinas in Paris 

with Albertus MsKnus. 
1940. Death of William 

of Auvergne (Bishop of 

Paris^. 
1952. Sccond residcncc of 

Aquinas in Paris of un- 

ccrtain duration. 
1958. Death of (irosseteste. 
1855. Konaventura bccomcs 

(Scneral of Franciscans. 
195B. Hagdad captured from 

Saraccns by Tartars. 
1905. Guy Fulcodi elected 

Pope Clement IV. 

1908. DcathofClcmentlV. 
1970. Death of Saint Louis. 
1974. Dcath of Bonavcn- 

tura ; Jerome of Ascoli 

becomes Gencral of 

Kranciscans. 
Death of Thomas 

Aquinas. 
(t)Birth of Duns Scotus. 
1980. Death of Albertus 

Magnus. 
1988. Jerome of Ascoli 

beci>mca NicoUs IV ; 

Ka>*mundo (talfredi suc* 

c«et)s him as (tencFaU 

1909. Dcath ot^ Nicolas IV. 



Statements rttting on laUr 
authority. 



1810-15. Born near II- 
chester in Dorsetshire, 
or, according to another 
tradition, in the parish 
of Bisley in Gloucester- 
shire. (Cf. Brewer, p. 
Ixxxv.) 



1940. Went from Oxford 
to Paris about 1240. 
Probably entered Fran- 
ciscan (3rder a few years 
later. 

1860-7. ProbablyinOxford. 
Legcnd as to Bacon's 
Tower may perhaps be 
rcferred to this period. 



1878. Imprisonment^rto^/rr 
novitaits suspectas^ 1278. 
^See Summa Historiidis 
ofAntoninus.Archbishop 
of Florence. a writer of 
the fifteenth centuiy.) 

1808. Release from prison 
probably 1993. Died 
1099 or 1994. Buried 
in Franciscan Church in 
Oxford. Legend as to 
exposure of his writings 
to wind and weather 
told by Wood. 



Fttctt veri/Udby Baeon^s staU- 

nunt or by amlemporary 

autltoriiy. 



1930. Michael Scot intro- 
duces his translations 
of Aristotle. {Op- ^V' 
vol. i. p. 55,) 

1238. Interview of Bacon 
with Henry III at Ox- 
ford, as described by 
Matthew Paris. 

1245. Heard William of 
Auvergiie (Bishop of 
Paris) lecture on rw- 
telUctus agens. [^Op. Tert. 
cap. 33.) 

1250. Saw the leader of the 
Pastoureaux marching 
through France in 1250. 
{Op. Maj, vol. i. p. 401.) 

1267. *Exile'from Oxford 
to Paris began. {Op* 
Tert. cap. i.) 

1258-^7. His family took 
the King*s side in war 
with barons. \Pp' Tert. 
cap. 3.) 

1284-5. Enters into rela- 
tions with Guy Fulcodi. 

1288. Bacon ordered to send 
his writings to the Pope. 

1288-7. Composition of 
Opus Majus^pus Minus, 
Opus TerHum. 

1288. DeathofCIementlV. 

1271. Writes the Compen- 
eHum Stuelti PhHosopiuae, 
denouncing the comip- 
ttonsoftheChurch. ^See 
Brewcr, p. liv.) 

1202. Writes Compen/hum 
Tkeotogiae, See MS. oT 
this work ^Br M. Royal 
7 F vii. foL 154). 



[ xix* ] 



NOTE. 

In the July issue of the English Historical Review, 1897, 
Dr. Gasquet publishes a MS. of Bacon which he has found 
in the Vatican, and which he inclines to think is a preface 
to the Ofms Majus, 

There is much to justify this view. The work in question 
describes Bacon's overflowing gratitude for Pope Clement's 
message to him; apologizes for the delay in the transmission 
of his works by pointing out that none of these works were 
in a complete state ; e;^p1ains the obstacles interposed by the 
distress of his family, ruined in the civil wars, and by the re- 
strictions of his Order ; introduces his disciple John, who had 
been for seven years under his tuition ; and finally concludes 
with a brief summary of the contents of the Opus Majus. This 
he describes, not as his principal work, but as a Persuasio, 
It has seven parts. After briefly noting the contents of the 
first two, Bacon passes to the seventh (published for the first 
time in this edition) and then comments successively on the 
sixth, fifth, fourth, and third. 

It will be observed by readers of this short treatise that it 
contains little that is not set forth with much greater fullness 
in the Opus Tertiuni, which is to be regarded as the real 
Introduction to the collection of writings sent by Bacon in 
1267 to Pope Clement IV. The first chapter of Dr. Gasquet's 
MS. is almost exactly identical with pp. 7-12 in Brewer's edition 
of Opus Tertiuntf the latter, however, having certain sentences 
not contained in the former. The fifth chapter is a repetition 
of Opus Majus^ pt i. cap. 16. One or two sentences, however, 
of this newly published work deserve attention. We learn 
from it that Bacon's life in Paris between 1257 and 1267 was 
a time of comparative inaction : a decent annis propter languores 



[ ^^* ] 

mtiltos et infirntitates varias ocaipationibus exterioribus studii non 
vacavi. He had written, he says, much before entering the 
Franciscan Order, with a view to the instruction of youth (multa 
in alio statu conscripseram propter juvenum rudimenta) ; and 
of late years he had sent fragments of his works to friends 
(aliqua capitula nunc de tina scientia nunc de alia ad instantiam 
amicorum aliquando more transitorio compilavi. No treatise, 
however, on any department of philosophy had been issued in 
a complete fomi. 

On the whole 1 am inclined to think that the short work 
edited by Dr. Gasquet is a first draft of what was afterwards 
expanded into the Opus Tertium. Bacon tells us that he was 
in the habit of writing his discourses several times over until 
they were brought into satisfactory shape. Sentiens meam 
imbecillitatem nihil scribo difficile quod non transeat usque ad 
quartum vel quintum exemplum anteqtiam habeam qttod intendo. 

J. H. B. 
July 21, 1897. 



Bacon^s Opus Majus,'] 



INTRODUCTION 



I. BACON'S LIFE. 

In considering the little that is known of the life of Bacon, 
it is well to give precedence to the few facts that are fixed 
with perfect precision by his own statement. We know with 
entire accuracy the date of the composition of the Opus 
Majus^ and of the two subsidiary works, the Opus Minus and 
the Opus Tertium. Pope Clement^ IVs instructions to him 
to transmit the results of his labours were issued June 22, 
1 266 from Viterbo. Within the year that followed, the Opus 
MajuSj with its supplement, the Opus Minus^ and its intro- 
duction, the Opus Teriium^ had been completed and sent to 
the Pope. At this time he speaks of himself as an old man, 
and he says that he had been studying language^ science, 
and philosophy for nearly forty years {Opiis Tertium^ cap. 20). 
From this it may be supposed that he was born between 1210 
and 1215. But the place of his birth cannot be said to be 
fixed with certainty. 

One, and only one, notice of his name occurs in a con- 

■ Guy Fulcodi (or Foulques), who succeeded to the Papacy in 1965 aa 
Cleinent IV, was bom at Saint Gilles in Languedoc He began his career by 
studying law, in which he achieved great distinction. He was married and had 
scveral children. He seems to have acted for some time as a private secretary 
to Louis IX. After his wife's death he entered the Church, was made arch- 
bishop of Narbonne in 1959, ^^ cardinal bishop of S. Sabina in ia6i. (Sec 
Fleuiy, Hist. Ecclisiastique^ liv. 85, whose spelling of the name Guy Fulcodi is 
here adopted.) Brewer conjectures (pp. xi et seq.) that he entered into 
relations with Bacon on the occasion of his mission to England as Pkpal legate 
in xa63 or 1364. But Bacon was then in Paris, and had becn tbere for several 
years. Guy Fulcodi had far better opportunities of hearing about Bacon in Paris 
than could have occurred during the time of his stormy and ineffectual legation 
to England. 



xxii INTRODUCTION. 

temporary writer. Matthew Paris relates, under the year 
1233, that Henry III convoked the counts and barons of the 
kingdom to a council at Oxford. Their animosity against 
Pierre des Roches, Bishop of Winchester, the king's chief 
adviser, who had surrounded his person with a body-guard of 
Poitevins and filled England with these foreigners, led them 
to refuse the summons. While the king was debating what 
measures to take against the recalcitrant barons, a Dominican 
preacher, Robert Bacon by name, told him frankly that there 
would be no hope of permanent peace in the kingdom so long 
as the Bishop of Winchester and his son, or kinsman, Peter of 
Rievaulx, retained power. Robert Bacon's opinion was echoed 
by others, and the king was induced to listen to it patiently. 

* Then a certain clerk who was present at the Court, Roger 
Bacon by name, a man of mirthful speech, said with pleasant 
yet pointed wit, " My lord king, what is that which is most 
hurtful and fearful to those that sail across the sea ? *' " Those 
know it," the king replied, " who have much experience of the 
waters.'* " My lord," said the clerk, " I will tell you ; stones 
and rocks"; meaning thereby Pierre des Roches.' It has 
been thought that the date of the dialogue was too early to 
refer to the Roger Bacon with whom we are here concerned. 
But since he might well be more than twenty years old at 
the time, the doubt seems hardly founded. 

What is certain from Bacon's own statement is that his 
family was one of some wealth, since he himself had been 
able to spend much money on experimental research. It 
appears also that this family had taken the royal side through- 
out the disputes between Henry and his barons, and had 
suffered pecuniary loss and exile for their loyalty. He tells 
Pope Clement that, being in sore distress for the money 
necessary for the transcription and conveyance of his MSS., 

* I wrote to my brother, a rich man in my country. But he, 
belonging as he did to the king's party, was in exile with my 
mother, brothers, and the whole family. Ruined and reduced 
to utter poverty, he was unable to help me, and up to the 
present day he has sent me no reply.' (Op, Tert, cap. 3 ) 

The forty years of study, of which he speaks in 1267, may 



BACON'S LIFE. xxiii 

be divided into two periods, apparently of nearly equal length ; 
the periods before and after his admission into the Franciscan 
Order. In the seventeenth chapter of the Opus Tertium he 
speaks of having devoted more than twenty years to the study 
of languages and of science. * I sought/ he says, * the friend- 
ship of all wise men among the Latins ; and I caused young 
men to be trained in languages, in geometrical figures, in 
numbers, in the constniction of tables^ in the use of instru- 
ments, and in many other necessary things. . . During this 
time I spent more than two thousand pounds in those things 
and in the purchase of books and instruments.' We may 
presume that the pounds were French, which at that time 
would correspond to between 6go and 700 pounds sterling. 
The sum was a lar^e one. And whether large or small, it 
would be quite incompatible with the profession of an Order 
specially devoted to poverty. It may be inferred, therefore, 
that since he had studied independently for some twenty 
years, it was not till some time between 1245 ^^^ ^^5^ ^^^ 
Bacon became a Franciscan. 

Among the men distinguished for their learning whose 
friendship he cultivated at this part of his career may be 
counted, in all probability, Adam de Marisco ; Edmund Rich, 
afterwards Archbishop of Canterbury and ultimately canonized ; 
Thomas Bungay, whose name was one day to be associated 
with his own as a worker of magic; Thomas, Bishop of 
St. David; John of Basingstoke, scholar and traveller; John 
Peckham, afterwards Archbishop of Canterbury ; Hermann, 
one of the principal translators of Aristotle; Shirwood, the 
treasurer of Lincoln; and last and greatest, the illustrious 
Bishop of Ltncoln, Robert Grosseteste. In Bacon's earlier 
years of study, Grosseteste had not plunged into the arduous 
and absorbing work of his episcopate. Noint scientias^ Bacon 
says of him. He was rector scholarum^ and also Chancellor 
of Oxford, and in 1224 was the rector of the Franciscans 
recentiy established there. The terms in which Bacon bears 
testimony to his encouragement of philology, to his attempts 
to apply mathematical method to the study of physical 
phenomena, to his disregard of the philosophy of the schools 



xxiv INTRODUCTION. 

as founded on bad translations of Aristotle (Brewer, Compend, 
Studii^ cap. 8), would be conclusive as to his personal contact 
with this great man, even though it were not confirmed by 
reference to Grosseteste's scientific writings, in which Bacon*s 
debt to him is unmistakable. His treatise De Physicis Lineis^ 
Angidis, et Figuris contains passages as to the spherical radia- 
tion of force, and as to the change in its direction by reflection 
and refraction, which bear a close resemblance to the lan- 
guage used many years afterwards by Bacon. 

It would appear that, at the beginning of the thirteenth 
century, there was a stronger impulse towards scientific study 
in Oxford than in Paris. In the eleventh chapter of the Opus 
Tertium, when speaking of the science of Optics, Bacon 
observes, * On this science no lectures have as yet been given 
in Paris, nor anywhere among the Latins, except twice at 
Oxford.' It is not stated that the lecturer was Grosseteste ; 
but we ma}' well believe it. It may be supposed that the 
influence of Adelard of Bath, the first translator of Euclid, had 
left its traces. Twenty years before the closc of the twelfth 
century we hear of two Englishmen, Alexander Neckham and . 
Alfrtd Sershall, lecturing in Paris on the Physics of Aristotle, 
then recently introduced from the school of translators from 
Arabic directed by Archbishop Raymond of Toledo. 

But the University of Paris, placed nearer the centre of the 
spiritual forces that swayed mediaeval society, had grown up 
under the dialectical influences of thcological controversy; 
and when Bacon went there, perhaps about 1240, he found 
what is called, vaguely and inaccurately enough, the scholastic 
philosophy in the fullness of its growth, with the enlarged 
scopc given to it by the recent permission to study the Physics,' 
Metaphysics, and Psychology of Aristotle. Its two most 
prominent representatives were at this time Alexander of 
Hales and William of Auvergne. Of the methods and the 
controversies then current Bacon made himself a master, and 
received the title of doctor. To be able to speak the languagc 
of the schools with authority was the first condition of obtain- 
ing a hearing. But he was not slow to perceive that the men 
who taught this philosophy were, for the most part, whoUy 



BACOirS LIFE. XXV 

destitutc of positive knowledge, They knew no language but 
Latin. Beyond the shreds of arithmetic, mensuration, and 
astronomy taught in the manuals of the Quadrivium, they 
were ignorant of mathematics, Of the possibility of applying 
mathematical knowledge to the facts of nature they had 
formed no conception whatever. Their philosophy was a 
tangle of barren controversies reducible, for the most part, to 
verbal disputes. It bore no relation to the facts of real life. 
It held out no hope of raising the Catholic Church to the 
position of intellectual domination needed for establishing her 
authority over the Asiatic world, from which dangers were 
looming of appalling magnitude. 

It was in Paris that Bacon came into contact with a remark* 
able man of whom very little would be known to us but for 
Bacon's eulcgies, Peter of Maricourt *, a native of Picardy. 
From the description given of him in the thirteenth chapter 
of the Opus Tertium, he would seem to have been an un- 
ambitious man, anxious only to pursue his researches in 
private, r^ardless of the metaphysical turmoil around him. 
Speaking of experimental research, Bacon says : * One man 
I know, and one only, who can be praised for his achievcments 
in this science. Of discourses and battles of words he takes 
no heed : he follows the works of wisdom, and in these finds 
rest. What others strive to see dimly and biindly, like bats 
in twilight, he gazes at in the fuU light of day, because he is 
a master of experiment. Through experiment he gains know- 
ledge of natural things, medical, chemical, indeed of everything 
in the hcavens or earth. He is ashamed that things should 
be known to laymen, old women, soldiers, ploughmen, of 
which he is ignorant. Therefore he has looked closely into 
the doings of those who work in metals and minerals of all 

' There is some doubt as to the orthography of the name, though none can 
now be left as to the idcntity of the person indicated. Emile Charles (pp. 16- 
17) mentions a MS. in the Paris library ( Biblioth^que Nationale, Manuscrits 
Latins, ^a-jB^ in which the only known work of Peter Peregrinus is spoken of as 
* Epistola Petri Peregrini de Maricourt ad Sygerium de Fontancourt de Magnete.* 
Charies adds that there is a village called Mehariscourt in Picardy ncar the 
abbey of Corbie. The Latin form of the word in one MS. of the Opus Tertium 
is written Maharncuria, but in others Mahariscuria. Cf. vol. ii. p. 303 of the 
present work ; see also BerteUi's DetiiMasicms Magtutica (Rome, 1893}. 



XXVI INTRODUCTION. 

kinds ; he knows everything relating to the art of war, the 
making of weapons, and the chase ; he has looked closely into 
agriculture, mensuration, and farming work ; he has even taken 
note of the remedies, lot-casting, and charms used by old 
women and by wizards and magicians, and of the deceptions 
and devices of conjurors, so that nothing which deserves 
inquiry should escape him, and that he may be able to expose 
the falsehoods of magicians. If philosophy is to be carried 
to its perfection and is to be handled with utility and certainty, 
his aid is indispensable. As for reward, he neither receives 
nor seeks it. If he frequented kings and princes, he would 
easily find those who would bestow on him honours and wealth. 
Or, if in Paris he would display the results of his researches, 
the whole world would foliow him. But since either of these 
courses would hinder him from pursuing the great experiments 
in which he delights, he puts honour and wealth aside, knowing 
well that his wisdom wouid secure him wealth whenever he 
chose. For the last three years he has been working at the 
production of a mirror that shall produce combustion at a fixed 
distance ; a problem which the Latins have neither solved nor 
attempted, though books have been written upon the subject* 
Of this remarkable man little is known but what Bacon 
tells us in the foregoing and other passages of the OptiS 
Tertiunty and the Opus Majus. But what we know is not 
inconsistent with Bacon's eulogy. Libri, in a note contained 
in the second volume of his History of Mathetnatics^ transcribes 
a letter written by Peter Peregrinus of Maricourt to a certain 
Sigermus of Fontancourt, which is a treatise on the properties 
of the magic stone, on the relations of its poles to those of 
the heavens and earth, on the way to find these poles ; on the 
repulsion in two magnets of poles of the same name, and the 
attraction of those of different names ; and on the construction 
of a globe which should revolve with the revolution of the 
heavens, and thus supply the place of the ordinary observation 
by the astrolabe. This is, no doubt, the invention of which 
Bacon speaks in the sixth part of the Opus Majus. Gilbert, 
in his great work on Magnetism, makes frequent mention of 
this treatise of Peter Peregrinus; and a careful comparison 



BACON'S LIFE. xxvii 

of the two works, separated as they are by an interval of 
more than three centuries, shows undoubted and weighty 
obligations of Gilbert to his predecessor. In the construction 
of globular magnets (the ' terrella,' or model of the earth), in 
the mode of finding their poles, the procedure, and indeed 
thc very language of Peter, is closely foliowed by the later 
inquirer. 

To a mind so original as Bacon's, trained in scientific method 
by Grosseteste and other members of the Engiish mathe- 
matical school, the influence of an experimental thinker 
iike Peter of Maricourt must have been stimul^ting in the 
extreme. Bacon was thirsting for reality in a barren iand 
infested with metaphysical mirage. From the horse-load of 
verbal controversies contained in the Summa of Aiexander 
of Hales, from the interminable series of tedious commentaries 
on Aristotle, of which so great a master as Albert was setting 
the first fatal example, he took refuge in the visions of the 
harvest of new truth that was to be reaped by patient observa- 
tion of Nature, by submission of her processes to experimental 
questioning, by following the lowly paths used by plain men 
in their daily avocations. * The wiser men are/ he said, * the 
more humbly will they submit to learn from others ; they do 
not disdain the simplicity of those who teach them ; they are 
willing to lower thcmselves to the level of husbandmen, of 
poor women, of children. Many things are known to the 
simple and unlearned which escape the notice of the wise. 
I have learned more important truth beyond comparison from 
men of humble station, who are not named in the schools, than 
from all the famous doctors. Let no man therefore boast of 
his wisdom, or look down upon the iowly, who have knowledge 
of many secret things which God has not shown to those 
renowned for wisdom ' {Optis Majns, vol. i. p. i o). 

Assuming that Bacon entered the Franciscan Order about 
1 247, he would bc at that time still in Paris. The degree of 
doctor, rarely conferred before the age of thirty-five, was 
probabiy received about the same time. He tells us {Opus 
Ttrtium^csip,2^) that he heard William of Auvergne lecturing 
to the University on the * active intellect/ Tliis must have been 



xxviii INTRODUCTION. 

before 1248, the date of Wiiliam's death. We know that he 
must have been still in France in 1 250, for in that year the 
revolt of the Pastoureaux broke out ; and Bacon tells us that 
he * saw their leader walking barefoot in a troup of armed men 
carrying something in his hands with the care with which 
a man carries a sacred relic ' {Opus Majus^ vol. i. p. 401). 

For some time between this date and 1257 he was probably 
10 Oxford. Whether he lectured there pubiicly we do not 
know. But that he incurred the suspicion of his superiors in 
the Franciscan Order is certain ; whether by audacity in speeu- 
lation, by e^periments looked upon as magical, or by frank 
exposure of the ignorance of professorial magnates, cannot be 
said with certainty. His old friends and teachers, Edmund 
Rich and Adam de Marisco, had passed from the scene. 
Grosseteste, his revered master, was dead, or died (1253) 
shortly after his return, in despair at the corruption of the 
Papacy, and half doubting whether Rome had not become 
the seat of Antichrist. No one was left to promote the study 
of Greek, which for aught we know died out in Oxford till 
Erasmus witnessed its revivaL In 1255, John of Fidanza, 
better known as Bonaventura, became General of the 
Franciscan Order, a man of exalted and aspiring mysticism, 
eager to revive the spirit of St. Francis, and not likely to 
care much for new learning that might lead he knew not 
whither. Perhaps it was byhis direction that Roger Bacon, 
about 1257, was removed from Oxford, and placed under 
close supervision in the Paris house. 

Wliat degree of restriction was placed upon his liberty is 
not very easy to define with precision. He was not forbidden 
to write, although he implies that he had not availed himself 
of the power to do so to any considerable extent. To multiply 
books by copyists was impracticable ; first, because copyists 
outsidc the Order could not be trusted to make an honest 
use of the copies at their disposal ; and secondly, because 
a strict prohibition was laid down and enforced against com- 
municating any manuscripts to those who were not members 
of the Order. When Pope Clement*s message reached him 
requiring him to transmit his works with the least possible 



BACON'S LIFE. xxix 

delay, these works for the most part were still unwritten. Never- 
theless there were exceptions. He had compiled, he tells us, 
from time to time, certain chapters on various subjects at the 
instance of friends (Opus Tertiuniy cap. 2). Among these 
chapters is probably to be reckoned the treatise De Multiplu 
catione Specierum^ which was sent to the Pope by the same 
messenger who conveyed the Opus Majus, though it does not, 
strictly speaking, form a part of that work. Careful examina- 
tion shows it to be a portion of the more complete philosophical 
treatise to the completion of which Bacon always aspired, till 
the time came, ten years afterwards, when his philosophical 
career was fatally arrested. Its style is diflerent from that of 
the other three treatises, Majus, Minus, and Tertium. It is 
not like these a Persuasio^ that is a more or less popular 
discourse addressed to a reader like Clement IV ; a reader 
of keen understanding doubtless, but at the same time the 
busiest man in Christendom. The Multiplicatio Specierum is 
a fragment of a systematic work written with full observance 
of philosophic language and of the dialectic of the schools. 

Whatever the discipline imposed during this period of his 
Wicy one important sphere of activity undoubtedly remained 
open to him. For many years he had been striving to form 
a school of young men, who should carry on the work which he 
had begun. We have seen in the treatise which throws so 
much ]ight on the details of his life {Opus Tertium^ cap. 17), 
that he had been engaged for a long time in instructing young 
men in languages, in gcometry, in arithmetic, in the construc- 
tion of tables, and in the use of scientific instruments. From 
this part of his work he was evidently not cut oflT during his 
life in Paris from 1257 to 1267. The messenger whom he 
selected to convey his manuscripts to Pope Clement was a poor 
lad whom he had been training in this way for five or six 
years. On the whole it seems probable that the restrictions 
placed on his liberty at this period of his life were not of 
extreme severity. 

Of thc reception given to Bacon's manuscripts in Rome we 
know absolutely nothing. A few months after their arrival 
Clement IV died ; and the papal see remained vacant for 



XXX INTRODUCTION. 

threc years. The Pope elected in 1271 (Gregory X) was 
a Franciscan. Owing his elevation to St. Bonaventura, he 
vvas not Hkely to show favour to a suspected member of his 
Order. Yet it was in this year or shortly afterwards that Bacon 
wrote the work known as Compendiutn Studii Philosophiae ^, an 
introductory discourse, perhaps,fortheencyclopaedic Srriptum 
PrincipaUy at the completion of which he was always aiming. 
In this treatise Bacon plunged into stronger invective against 
the intellectual and moral vices of his time than he had ever 
used before. In no previous writing had the moral corrup- 
' tion of the Church, from the court of Rome downwards, been 
so fiercely stigmatized ; * the whole clergy is given up to pride^ 
luxury, and avarice. Wherever clergymen are gathered to- 
gether, as at Paris and Oxford, their quarrels, their contentions, 
and their vices are a scandal to laymen.* Unbridled violence 
among kings and nobles, fraud and falsehood among trades« 
men and artificers were the inevitable result. Progress in 
wisdom was hopeless when the moral condition of those who 
should promote it was so far below that of the teachers of the 
pagan world Unless sweeping remedies were applied by 
a refonning Pope, there was no prospect but the advent of 
Antichrist in the near future (Brewer, pp. 399-404). 

Perhaps even these denunciations roused less antagonism 
than the sweeping attacks on the scholastic pedantry of his 
contemporaries, their false conceit of wisdom, and their pre- 
ference of metaphysical subtleties and verbal strifes to the 
pursuit of real knowledge. Of these charges his previous 
writings had been full, but they were now renewed and 
emphasized. Aristotelian study, which at the beginning of 
the century had been the great stimulant of thought, was 
already becoming the great obstruction, and was preparing 
for the next century a reign of darkness. Based on false and 
ignorant translations, it were better, Bacon said, to do away 
with it altogether than that it should be carried on by men 
ignorant of the language in which Aristotle wrote, and 
destitute of the scientific training which alone could qualify 
them for explaining him (Brewer, pp. 469-473). 

* Contained in Brewer*s work, pp, 393-519. 



BACON'S LIFE. xxxi 

The storm of indignation had long bcen gathering : and in 
T277 it broke. In that year Jerome d'Ascoli, who four years 
before had succeeded Bonaventura as General of the Franciscan 
Order, held a chapter in Paris. Bacon was summoned on 
account of * certain suspected novelties.' He was condemned, 
and thrown into prison. What were the 'novelties' that 
constituted his crime we do not know. His works abounded 
in them. It was not perhaps difficult to show that he had 
gone too far in connecting changes in reh*gious faith with 
conjunctions of Jupiter and Mercury ; and in hinting that 
underneath the jugglery of the magicians, valuable truths 
might sometimes lie conceaied. The real motives for stifling 
his voice lay far deeper. 

That he should have held the history of Greek philosophy 
to have been under the keeping and guidance of Providence 
no less than the history of Judaea; that he should have 
regarded the teaching of the StoLcs on personal moraHt}" as 
superior to that of any Christian teacher ; that he should 
have dwelt with such frequent emphasis on the ethical value 
of Mohammedan writers like Alfarabius, Avicenna, and 
Algazel — these were things likely to startle even the most 
tolerant and thoughtful of his contemporaries, much more 
the common average of his Order, who had suspected him 
of unsound views for twenty years. Not indeed that his 
career would have been impedcd by the fact that the founder 
of the Franciscans had shown disregard, if not dislike of 
worldly knowledge. Alexander of Hales had jolned the 
brotherhood before the death of St. Francis, and had 
dominated the schools of Paris long before the voice of 
Albert had becn heard there, and while Aquinas was a child. 
To a man of ordinary temper, addicted to bold speculation, 
the protection of so powerful a corporation as the Francis- 
cans had become when Bacon joined them would have been 
invaluable. But Bacon threw his chances away. He attacked 
the celebrities of his own Order as severely as those of its 
rival. His fiery and impatient spirit was to be bound by no 
shackles of prudence. He had come to Paris fresh from the 
teaching of men Uke Grosseteste, eager for the promotion 



xxxii INTRODUCTION. 

and diffusion of science, no less than for the reform of the 
Church. He found the great university immersed in dialcc- 
tical controversy. Many of the controverted qucstions were 
of momentous importance, and Bacon was prepared to take 
his part in them. But they were prosecuted by men devoid 
of scientific training, unprepared thcrefore to distinguish 
truth from error, verbal subtleties from fundamental realities ; 
unwiliing even to take the trouble to study Aristotle and 
the Bible in their original language. He saw that philosophy 
without science could not fail to degenerate (as history, ancient 
and modem, shows that it always has degenerated) into 
academic pedantry, and would confirm that one of the aber- 
rations of intellect which he looked on as the worst and the 
most fatal, the false conceit of knowledge. Against ignorance 
under the cloak of wisdom he urged, like Socrates, a lifelong 
war ; and, like Galileo, he met with a worse fate than that of 
Socrates, the martyrdom of enforced silence. 

No crusade has been conducted by blameless crusaders. 
It cannot be denied that Bacon's indiscriminatin^ zeal in- 
cluded, with pedants and obscurantists who were his lawful 
prey, two men who were his equals, one of them, perhaps, his 
superior. Albert was a student of nature as well as a philo- 
sopher. Aquinas, as a student of man and of society, and 
as the constructive thinker who gave coherency to the vast 
fabric of Catholic discipline, achieved results which, judged at 
the distance of six centuries, Bacon neither equalled nor 
approached. Jealousy of the rival Dominican Order, of 
which these men were the chief ornaments, cannot account 
for Bacon s failure to recognize their vaiue ; for the Irre- 
fragable Doctor, Alexander of Hales, was a Franciscan, and 
was criticized more harshly than either. In their failure to 
appreciate duly the importance of scientific culture as a basis 
of Cathoiic action on a doubting and unbelieving world, 
the doctors of the Paris schools were ali alike involved in 
his unmeasured strictures. We may understand, though we 
cannot justify, his impatience. He has bitterly expiated it by 
many centuries of neglect. 

It can hardly be doubted that the seclusion consequent 



BACON'S LIFE. xxxiH 

on his condemnation in 1^77 was effective and rigorous. 
Appeals to the Pope had been anticipated by Jerome, who 
took care to impress on the court of Rome the expediency 
of confirming his decision. AU hopes of completing the 
Scriptum Principale were shattered. He remained a prisoner, 
so it is thought, for fourteen years. Jerome meantime had 
become Pope Nicholas IV. After his death in 1292, 
a chapter of the Franciscans was heid in Paris, at which 
Raymond Gaufredi, then General of the Order, set free some 
of those who had been condemned in 1277. ^t may be 
looked upon as nearly certain that Bacon was of the 
number. Certain at ieast it is from his own words that in 
that year he was again at work, on his last treatise, the Com" 
pendium Theologiae^ in which the date 1292 is expressly 
mentioned. Whether he died in this year, or two years 
afterwards. is uncertain. He was buried in the Franciscan 
church in Oxford. 

The legend that his works were nailed to the walls of the 
library and allowed to perish ignominiously may be dismissed. 
But that his life-long efforts to establish a Catholic school of 
progressive iearning utterly failed, there can be no doubt 
whatever. Such men as Rich, Grosseteste, and Bacon, were 
not seen at Oxford in the fourteenth century. Greek, mathe- 
matics, and experimental science were overwhelmed in the 
paralyzing mists of Scotian dialectic, Nevertheless it would 
be an error to suppose that his life-work was a failure. 
Here and there throughout Europe the tradition of the Doctor 
Mirabilis survived as a stimulating force, and kept the embers 
of scientific study alive tili the time of the Renascence. 

In proof of this, three instances may be given : — 

I. Peter d'Ailly, in his Imago Mundiy written early in the 
fifteenth century, discussing the relations of the extreme east 
and west of the habitable globe, has a long passage treating 
of the probable proximity of Spain and India. For all that 
appears in the work this passage is his own. But in fact it is 
a verbal quotation from the fourth part of the Opus Majus^ 
voL i. p. 290. And it has a history worth recording. For it is 
cited in J498 in a letter from Columbus to Ferdinand and 

VOL. I. c 



xxxiv INTRODUCTION. 

Isabella, as one of the authorities that had put it into his mind 
to venture 6n his great voyage. 

2. John Dee. in a memorial addressed to Queen Elizabeth 
in 1582 on the reformation of the Calendar, speaking of 
those who had advocated this change, says* : * None hath done 
it morc eamestly, neither with better reason and skill, than 
hath a subject of this British Sceptre Royal done, named as 
some think David Dee of Radik, but otherwise and most 
commonly (upon his name altered at the alteration of state 
into friarly profession) called Roger Bacon: who at large 
wrote thereof divers treatises and discourses to Pope Clement 
the fifth {sic) about the year of our Lord 1267. To whom 
he wrote and sent also great volumes exquisitely compiled of 
all sciences and singularities, philosophical and mathematical, 
as they might be available to the state of Christ his Catholic 
Church/ Dee proceeds to give extracts from Bacon s works 
in proof of these assertions ; and remarks that Paul of Middle- 
burg, who was much occupied with the question of the Calen- 
dar, and had treated of it in his work Paulina de recta Paschae 
celebratione, had made great use of Bacon. * His great volume 
is more than half thereof written (though not acknowledged), 
by such order and method generally and particularly as our 
Roger Bacon laid out for the handling of the matter.* When 
we remember that it was Paul of Middleburg by whom 
Copernicus was urged with a view to this very problem to 
construct more accurate astronomical tables, we shall gladly 
acknowledge that here, too, Bacon's labour was not lost. 

3. No part of Bacon*s work was more frequently transcribed 
than his Perspectiva* Based as it was upon the great work 
of Alhazen, which was itself a development of the Optics of 
Euclid and Ptolemy, and claiming indeed to be but an 
abridgement or condensation of the truths laid down by his 
predecessor with wearisome copiousness, it was in fact much 
more than this. It selected from a mass of propositions, 

' Dee*s memorial is contained among the Bryan Twyne MSS. in Corpus 
Christi College, Oxford. The supposition that Roger Bacon changed his name 
itrancp into the Franciscan Order appears to rest on no authority but that 
LO Dec's very erratic imagination. 



BACON'S LIFE, xxxv 

many of them mere displays of geometrical ingenuity, pre- 
cisely those which aimed at the interpretation of nature, and 
at the adaptation of the laws of luminous radiation to human 
purposes. He was aware of what was unknown to Ptolemy 
and Alhazen, the concentration of parallel rays from reflecting 
surfaces formed by revolutioas of a conic section ; though how 
far he was indebted for this knowledge to Peter Peregrinus 
or to Vitello cannot be stated with certainty. Of the magnify- 
ing powers of convex lenses Bacon had a clear comprehension. 
He imagined^ and was within measurable distance of eflecting, 
the combination of lenses which was to bring far things near, 
but which was not to be realized till the time of Galileo. 

In 1614, four years after the invention of the telescope, 
Combach, professor of philosophy in the University of Mar- 
purg, published this great work of Bacon, * viri eminentissimi/ 
It would be interesting to know whether the allusion in the 
Novutn Organutn (lib. i. 80) to the work of an obscure monk 
(* monachi alicujus in cellula') has reference to this work. The 
Cogitata et Visa was written before Combach's edition was 
published ; but examples of the Perspectiva were numerous, 
and it can hardly have been unknown to Francis Bacon. In 
any case it must have been known to Descartes, to whose 
epoch-making researches on Dioptrique it assuredly contributed 
a stimulating influence. This at least they have in common, 
that light is looked upon as correlated with other modes of 
propagation of force through the Ether. 

With the scientific Renascence of the sixteenth century, 
Roger Bacon^s name slowly emerged from the darkness which 
had enwrapped it for three centuries. Astrologers like Dee, 
Heyden, and Allen hailed him as a champion of their out- 
wom creed. Men of greater mark and sounder judgement, 
like Selden and Mead, were struck by his emancipation from 
the pedantry of the schools, and by his forecasts, made at so 
remote a time, of an age of industriai and scientific discovery. 
His central aim, the enlistment of progressive intellect in the 
cause of moral and religious renovation, was appreciated by 
none. But since the publication of his principal work in the 
eighteenth century, his name has gradually ascended towards 

c 2 



xxxvi INTRODUCTION. 

its permanent position, on the iofty summits which were the 
earliest to ^ take the moming ' of European thought. 



11. Bacon's Position in the Metaphysical Contro- 

VERSIES OF THE THIRTEENTH CENTURY. 

It is too often forgotten that Bacon was a schoolman ; 
trained in scholastic methods, and ready to take part in the 
phiiosophic discussions which interested his contemporaries. 
It is not perhaps surprising that this side of his work should 
have been ignored; for in the Ofus Majus, though visible 
enough to an attentive reader, it is thrown into the shade by 
the prominence given to positive science, and by the practical 
application of science to poh'tical and religious purposes. 
Certain chapters of the Opus Teriium^ which supplement too 
hasty or imperfect treatment in the larger work (chapters 
38-52), afford better illustrations of Bacon's aptitude for 
metaphyslcal discussion. Nevertheless, the position of Bacon 
in the scholastic controversies of the thirteenth century 
remained an unknown quantity till the appearance of Professor 
Charles s monograph. His comprehensive survey of Bacon's 
unpubh*shed works includes a careful study of, and copious 
extracts from the important fragment of the Scriptum Princi' 
pale^ entitled ' Communia Naturalium/ of which copies exist 
in the Mazarine library in Paris and in the British Museum. 

Haur6au's comprehensive work on Scholastic Philosophy hdiS 
made it easy to refute the illusion, still,however,not entireiy dis- 
sipated, that scholasticism implies a special set of philosophical 
tenets or an uniform method of treatment. Philosophical writers 
inthe thirteenth ctntury differed from one another no less than 
philosophical writers in the nineteenth ; though in either case 
a certain similarity in the subjects considered, and in the mode 
of handling them, was impressed by the circumstances of the 
time. Scholastic philosophy means simply philosophy taught 
in mediaeval schools. And between the schools of the twelfth, 
of the thirteenth, and of the fourteenth centuries^ there were 
great and essential differences. 



POSITION AMONG SCHOOLMEN xxxvii 

To pass from the reading of the Polycraticus of John of 
Salisbury, who knew nothing of Aristotle but his logic, and that 
imperfectly, to a treatise of Albert or of Aquinas seems, and 
is, a transition quite as abrupt as to exchange a volume of 
Addison or Swift for one of Schopenhauer or Carlyle. In the 
one case as in the other, a tide of revolution had swept between 
thecenturies. For it was nothing less than a revolution for the 
western mind to receive very suddenly from the Mohammedan 
world the results of three centuries of Arabian learning, includ- 
ing as it did ali the more serious part of Aristotie's work, 
enriched with keen-witted and audacious comment, and accom- 
panied by the scientific results of the schools of Alexandria ; 
the Syntaxis of Ptolemy and the biology of Galen. 

Isolated thinkers like Adelard of Bath^ the first transiator of 
Euc]id into Latin, had already entered this field of study, when 
Raymond, archbishop of Toledo, established in the middle 
of the twelfth century a systematic school of translators 
from the Arabic.of whom the Jew, John Avendeath (other- 
wise known as Johannes Hispalensis), Dominic Gundisalvi, 
archdeacon of Segovia, the translator of Algazel, and Gerard 
of Cremona, best known by his translations of the Almagest 
and of Alhazen, were the most prominent representatives *. 
Their translations of Aristotle, including his Physics, Meta- 
physics and Psychology, were not long in finding their way 
across the Pyrenees. Alexander Neckham, afterwards abbot 
of Cirencester, lectured upon them in Paris in 1180. His 
junior contemporary and countryman, Alfred of Sershall, 
pursued a similar course. Neither of these men roused 
suspicion. But the case was far otherwise with David of 
Dinant and Amaury of Bennes. Though we know little 

' See Jourdain, Rtchgrckss sur fdg€ tt torigine des tmductioHS Latiitts 
d*Aristot€, pp. 107-124 (ed. 1843). The history of mediaeval translations from 
Greck into Arabic, sometimes through intermediate Syriac versions, and 
from Arabic into Latin, deserves more elaborate treatment than it has yet 
received ; provided always that the writer of such a history combined the two 
cooditiona so constantly insistcd on by Bacon : knowledge of the languages 
concemed and knowledge of the subjects treated. Meaiitime much useful 
prctiininary work has i>een done in this direction by such writers as Wuesten> 
feJd and Jourdain. 



xxxviii INTRODUCTION, 

of either, except through the criticism of their opponents, 
notably through that of Albert and Aquinas, yet such criti- 
cism is too detailed and definite to admit of doubt that their 
deductions from Aristotle and from his Arabian commen- 
tators led them to the assertion of the unity of substance ; 
in other words, to the ultimate identity of matter, mind, and 
God. As quoted by Albert, the language of David was: 
*It is manifest that there is one soie substance, not only 
of all bodies, but also of ali souls, and that this is nothing 
but God himself. God, matter, and mind, are one and the 
same sole substance* (Albert. Summa Theolog, part II. 
tract. xii. quaest. 72, memb. 4, art. 2). David kept himself 
within the limits of philosophic theory. He is said to have 
been personally intimate with Innocent III; and at least 
during his lifetime his heresies escaped notice. It was 
otherwise with his contemporary Amaury of Bennes, who, 
maintaining the same opinions, was condemned by the Pope 
and forced publicly to disavow them. But they survived in 
his discipies, who used them in ways directly hostile to 
Catholic faith and discipline. A Councii was held in Paris 
in 1210. Amaurys body was disinterred and buried in un- 
consecrated ground ; several of his foUowers were bumt. It 
was at this council, the decrees of which were confirmed and 
enforced five years afterwards by Robert de Cour^on, the 
papal legate, that the study of the Physic and Metaphysic of 
Aristotle was prohibited, on the mistaken supposition that 
the ultimate source of these heresles was to be found there ; 
a mistake due probably to the comments of Averroes, with 
which the first translations of these works into Latin were 
accompanied *. 

How to deal with the problem of matter so as to give no 
countenance to pantheistic error, was therefore an urgent and 
momentous question, to which the schoolmen of the thirteenth 
century, and Albert especially, devoted their full powers. 

^ See Jean de Launoy's work De varia AristoUlis in Academia Parisiensi 
fortuna liber (Paris, 1653), in which seven stages are noted, from thc condemna- 
tion of Aristotle in 1309, to the condemnation of his opponents by the Parlement 
of Paris in 1604. Cf. Haur^au, Hist, de la Phiios, Scolast., Part II. vol. IL 
-1. 73-119- 



POSITION AMONG SCHOOLMEN xxxix 

Terrestrial substance, said Aristotle, was made up of matter 
and form. Apart from form, what then was matter ? A pure 
essence, having the capacity, /^/^«//V?, to become the subject of 
form, was thc repiy. How, then, distinguish matter from this 
potentia ? Yet, if this be so, if matter is potentially the subject 
of all possible forms, we have in matter something that under- 
lies all substance. Suppose all forms destroyed, matter holding 
in itself all the conditions of existence stili remains. How, 
then, distinguish matter from God ? 

Albert's attempted solution of the problem is involved and 
obscure in the extreme, and it must not occupy us here. We 
are concemed with Bacon's. Bacon attacked the problem in 
his own way, and with a full sense of its importance. His 
conclusions are expressed in the seventh chapter of the fourth 
part of the Opus Majus, and in the thirty-eighth chapter of 
the Opus Tertiutn ; and a still further exposition of them is 
found in the unpublished work of Bacon already mentioned, 
entitled * Communia Naturalium.' This treatise on Physical 
Philosophy consists of four parts, of which the discussion of 
Matter occupies the second. 

Substance, Bacon maintains, can be predicated neither of 
matter nor of form ; but only of the compound which results 
from their union. * Compositum habet rationem per se exis- 
tendi in ordine entium : non sic materia et forma.' Matter and 
form are not substances : substance results from thcir union. 
Proceeding from above downwards through the hierarchy of 
being in the ordcr of increasing speciality, we have, as the 
genus generalissimum, 'Substantia composita universalis.' 
This may be corporal or spiritual. Corporal substance may 
be terrestrial or celestial. Terrestrial substance may be 
a mixture of elements, or a single element. Mixed substance 
may be animate or inanimate. Animate substance may be 
sensitive (i.e. animal) or vegetal. Animal substance may be 
rational or irrational. 

To each of these grades in the hierarchy of substance belong 
corresponding grades, not merely in the hierarchy of form, but 
also in the hierarchy of matter. * Matter,' says Bacon, ' is not 
what most teachers of philosophy maintain it to be, ''una 



xl INTRODUCTION, 

numero." In the descending scale from general to special, 
each grade of matter, like each grade of form, is distinct from 
the preceding. One kind of matter is separated from another 
by specific differences, just as form is separated from form. 
The difference between an ass and a horse is not a difference 
of form only ; it is a difference of matter ' (* Commun. Natur.' 
Part II. Dist. ii. ch. 6). 

Bacon has condensed these views in the diagrammatic form 
shown in the subjoined schedules, which I have copied from 
the Mazarine MS. pp. 23, 24. (They have been coUated with 
those of the Br. Mus. MS. Royal, 7 F. vii. fol. 91 and 92. 
The variants in this MS. for the schedules oi subsiantia cotH' 
posita and forma are unimportant. Those of materia are 
omitted ; this MS. being in other respects less perfect than 
that of the Mazarine library.) 

How are we to estimate these speculations ? It is obvious 
in the first place that they stand in marked opposition to, or 
at least in distinction from, theories current among Bacon's 
contemporaries. To judge rightly of them we must bear in 
mind that throughout the greater part of the thirteenth 
century questions were being agitated of even greater impor- 
tance than the controversy between realism and nominalism. 
The pantheistic tendencies discernible in Averroes and other 
Arabian thinkers had been diffused, as we have seen, by men 
like Amaury and David of Dinant They were responsible, 
as some thought, for the disastrous anarchy which early in 
the century had devastated southem France. Bacon was 
quick to perceive the danger of maintaining the unity of 
matter, It had been defended, as he points out {pp. Maj\ 
vol. i. p. 144), by passages from Aristotle which he wishes to 
believe had been badly translated. In any case, he says, 
* the error is enormous, as great as any that can possibly be 
found in speculative questions. If it be granted, it is im- 
possible to comprehend the generation of things, and the 
whole course of nature will be misunderstood. And what is 
more, if this error be looked at closely, it will be found to 
tend towards heresy, or rather to be the profanest of heresies, 
since the inevitable result of it is to endow matter with the 



DlVISlO SUBSTANTIAE OOMPOSITAE UNIVER8A1.IS. 




[W./. Tofacep, xl.j 



DlVISIO FORMAE UNIVER8ALI& 




DlVlSIO MATERIAE PRIMAE UNIVERSALI8. 




POSITION AMONG SCHOOLMEN. xli 

creative power of God/ Whatever dangers were involved in 
the unity of matter, Bacon met by a bold denial of such 
unity. * Divide et impera/ he said in effect ; matter, thus 
split up into sections, is no longer to be feared. 

Looking at Bacon*s theory by the light of subsequent cen- 
turies, it is not difficult to see that its value lay in its solvent 
and destructive power. His aim from b^inning to end of 
his career was to draw men away from verbal subtleties and 
concentrate them on the realities of life, as plain men under- 
stand them. 'You ask me/ he would say to the young 
students around him, ' what is this matterwhich remains apart 
from all form, with capacity for receiving all ? But who told 
you that it was one and indivisible ? There are as many kinds 
and degrees of matter as there are of things. Look at the 
things, try them, see how they act on you, how you can act 
on them. As to the matter and form that may underlie 
them, leave that to God.' 

Bacon's part in the great controversy between realism and 
nominalism will lead us to a similar conclusion. It was a less 
burning controversy in the thirteenth century than in the days 
of Roscelin and Abelard, or than it became afterwards in the 
days of Duns Scotus and William of Ockham ; and it was 
debated by Albert and by Aquinas with the far larger and 
deeper understanding of its complications, that might be 
cxpected from men who were not merely trained like their 
predecessors in the study of AristotIe's Logic, but had become 
conversant with the problems raised in his Physic and 
Metaphysic. Both these thinkers rejected the independent 
existence of universals in re as clearly as Aristotle had 
done. They were clear that universals had no existence 
except in the mind. * Non est universale nisi dum intelli- 
gitur ' ( Albert. Met. lib. v. tract. vi. cap. 7). * Una et eadem 
natura quae singularis erat et individuatur per materiam in 
singularibus hominibus efficitur postea universalis per actionem 
intellectus depurantis illam a conditionibus quae sunt hic et 
nunc ' (Aquinas, Tractatus primus de umversalibus). Never- 
theless, both of them left a place for the universal ante rem^ 
not indeed in the fantastic world of Ideas which Plato had 



xlii INTRODUCTION. 

portrayed, but as radiations centred in the primal form, the 
mind of God. 

Turning to BacQn, who discusses the question of universals 
at considerable length and with extreme independence, we 
find the same tendency to emanctpate himself from bondage 
to words, entities, and verbal discussions, and to dig down to 
a foundation of solid fact. One individual, he says*, is of more 
account than all the universals in the world. A universal is 
nothing but the similarity of several individuals ; ' convenientia 
plurium individuorum.' * Two things/ he goes on to say, 
'are needful for the individual. The first is absolute: it 
is that which constitutes his existence, as when we say, 
''This man is made of soul and body." The second is 
that in which he resembles another man, and not an ass or 
a pig. This is his universal. But the absolute nature of an 
individual is of far more importance than his related naturc. 
It is fixed and absolute by itself. Thus the singular is of 
more account {nokilius) than its universal. Experience leads 
us to this conclusion, and so also does theology. God has 
not created the world for the sake of the universal man, but 
for the sake of individual persons.' * Individuum est natura 
absoluta et fixa habens esse per se ; et universale non est nisi 
convenientia individui respectu alterius,' 

In some passages Bacon appears to go much further in 
the direction of nominalism than Albert and Aquinas. ' The 
prevalent view,' he remarks, * is that universals exist only in 
the mind. Yet two stones would be like one another, even 
though there should be no mind to perceive them. But it is 
precisely this likeness of the two stones that constitutes their 
universar (* Commun. Natur.' Part II. Dist. ii. ch. lo). 

Closely allied with the controversy as to universals was the 
question of Individuation. Are things individualized by form 
or by matter? Albert and Aquinas took the latter view, 
Bonaventura the former. ' Individuorum multitudo,' says 
Albert [De Coelo, tract. iii. c. 8), * fit omnis per divisionem 
materiae. Formae quae sunt receptibiles in materia indivi- 

* On the question of Universals, and also on that of Individuation, cf. the 
extracts from the Cwnmunia NatHralium given by ^mile Charles, pp. 383>386. 



SCRIPTUM PRINCIPALE, xliii 

duantur per materiam.' (Cf. Aquinas, Suntma Theol. i. quaest. 
iii. cert. 2.) Aquinas was obliged, however, to add that this 
materia must be * signata ' : must be quantified. ' Signatio ejus 
est esse sub certis signationibus quae faciunt esse hic et nunc' 
This addition went far to neutralize the Thomist view of 
Individuation ; for as his opponents at once rejoined, * What 
determines quantity if not form ? ' 

In opposition to Aquinas, Bonaventura maintained that 
'species est totum esse individui.' Substance consisting of 
the union of matter and form, matter was uniform in all : the 
form was that which distinguished, individualized. 

Bacon (* Commun. Natur.' Pt. 1 1. Dist. ii. ch. 9), in opposition 
to either vtew, maintained that the question was meaningless 
and foolish. All substances, whether universal or singular, 
have their own constitutive principles. Soul and body make 
man. This soul and this body make this man. In the inten- 
tion and procedure of nature, ' this man ' is prior to ' man ' ; 
'man' comes in as something subsidiary, 'extra essentiam 
ejus, similis accidenti,' as the means of comparison with other 
individuals. There is no more reason for inquiring what 
causes individuation than for inquiring what causes universality. 
There is no answer to such a question, except that the Creator 
makes everything as its nature requires. Individual matter 
and form is made in one way : specific or generic matter and 
form is made in another. * Stultitia magna est in hujusmodi 
quaestione quam faciunt de individuatione.' 

III. Bacons *Scriptum Principale.' 

The foregoing remarks, which it would be easy, but not, in 
this place, justifiable to prolong, will illustrate Bacon's position 
as a schoolman, thoroughly versed in the technique of scho- 
lastic controversy. But he was a schoolman whom a long and 
laborious study of the realities of life, whether in nature or in 
man, had taught to distinguish things from words : solid facts 
from subtle iigments. He was not alone in this. Albert and 
Aquinas were solid thinkers like himself. Less versed in 
natural scicnce than Bacon, they had more than he to do 



xliv INTRODUCTION. 

with the science of man ; they had to face the difficult and 
urgent problems connected with the spiritual government of 
mankind. Their philosophy, like his, deait with real things. 
And if theirs was less positive, less free from metaphysical 
figments, it is only that the complications of human nature 
were less adapted for positive treatment than the physical 
phenomena to which Bacon devoted so large a share of his 
attention. 

But in contrast with these three great schoolmen stand the 
weavers of word-systems, like Alexander of Hales, Henry of 
Ghent, and Duns Scotus, wasting their own and other men's 
tlme and energy in defining, dividing, and refining with infinite 
ingenuity, and with such result as when children build sand- 
castles on the shore. With such men it may have been 
needful to fight, yet fighting was but beating the air. Of 
what avail to discuss Individuation with dialecticians who 
explained it by * haecceiias ^ ' ? 

In all Bacon's discussion of scholastic problems, the solution 
he reached was of a kind to favour the falling ofTof the meta- 
physical husk, and to bring to light the real and positive 
problem which lay beneath it. His scholastic theories are 
therefore for us, and in all probability were for him, of far 
greater ncgative than constructive value. But his central aim 
lay in another direction above and beyond scholasticism. We 
shall best learn how to appreciate it by looking at the pro- 
gramme of the encyclopaedic work, the * scriptum principale,' 
often spoken of in the Opiis Majus and the Opus Tertium^ but 

* This word is believed to be due rather to the disciples of Duns Scotus than 
to the master himself. Happily for Bacon*s peace of mind, he did not live to 
witncss thc triumphal career of the Doctor Subtilis. Of Haur^u^s careful 
appreciation of his work the final words may be quoted : ' Cette philosophie 
n'explique pas la nature, elle Tinvente ; substituant Tordre rationnel k Tordre 
r^el, elle dispense, il est vrai, de Tetude des choses ; mais, quand apr^s avoir 
admire T^conomie d'un syst^me si complet, si habilement ordonn^, on abaisse 
ses regards vers ces choses dont on a jusqu'aIors d^daigne de s'enquerir, on 
soup9onne d^s Tabord qu'on vient d'achever un r6ve, et bientdt, devant le 
spectacle qu^olTre la r^alit^, s^effacent, s*^vanouissent l'une aprte Tautre toutes 
les abstractions decevantes, toutes les chim^es dont la cr^ation appartient au 
syst^me, a lui seul/ \Hisi. dt la PhHos, SckoUtstiqut, Part H. vol. ii. pp. 171- 
959, ed. 1873-80.] 



SCRIPTUM PRINCIPALE. xlv 

of which the persecutions and imprisonment of his later life 
never allowed him to execute more than a few fragments. 
And of these fragments many are lost. 

This * scriptum principale,' as he tells us in the first chapter 
of the unpublished work entitled 'Communia Naturalium/ 
consisted, or was intended to consist, of four volumes. The 
first volume dealt with Grammar and Logic, the second with 
Mathematic, the third with Physic, the fourth with Metaphysic 
and Morals. 

The second chapter of the * Communia Naturalium'is entitled, 
' De universo ordine scientiarum naturalium.' He distinguishes 
eight natural sciences. The first treats of the principles 
common to Natural Philosophy. The others are: — (i)Per- 
spective or Optic, (a) Astronomy, (3) Barology, (4) Alchemy, 
(5) Agriculture, (6) Medicine, (7) Experimental Science. The 
general principles of Physics form the subject of the first 
treatise here spoken of. Of the seven special sciences, the 
first three form part of what would in the present day be 
called Physics. Under Astronomy is included not merely the 
study of planetary motions, but the scientific dctermination of 
terrestrial positions, in Other words, Geography, and also the 
influence of the stars and the sun on the earth and man: 
that is to say, the study of climate and of astrological forces. 
As to the third of the special sciences, * scientia de elementis,' 
or as he also calls it, 'scientia de Ponderibus,* what in the 
present day would be called Barology, it is not without 
interest to find it thus set apart as a distinct department of 
speculation. The fourth, Alkimia, corresponds, so far as the 
description of its purpose goes, very nearly to the modern 
science of Chemistry. It deals, says Bacon, with the ' mis- 
tiones elementorum/ with the generation of liquids, gases, and 
solids ('humores et spiritus et corpora'), with all inanimate 
substances, including organic products (' usque ad partes ani- 
malium et plantarum inclusive '). 

The title of the fifth science, Agricultura^ would be mis- 
leading, if Bacon had not given us a clear explanation of its 
purpose'. It is the science of living bodies, vegetal and 

' CC the long extract givcn by Charles, pp. 370-374. The unfortunate rarity 



xlvi INTRODUCTION. 

animal; reserving, however, the subject of man*s physical 
nature for subsequent treatment under the head of medicine. 
Before man be properly investigated, we must know the 
nature and surroundings of other animate things. First we 
must distinguish the soil fit for differcnt* kinds of plants, 
arable land, forest land, pasture land, garden land. We then 
examine thc whole subject of plants which has been left in- 
complete in the treatise attributed to Aristotle,/?^ Vegetabilibus, 
But as lands cannot be tilled without domestic animals, and 
as forests, pastures, and deserts depend for their value on the 
wild animals they contain, the science we are now speaking of 
embraces the full consideration of animal life on which, as 
Bacon believed, Aristotle wrote far more volumes than have 
come down to us In the sixth science we proceed to the 
study of the animal possessing reason, the study of Man. 

of Charles* work is my excuse for citing the portion of this extract relating to 
the study of living bodies, based, as Bacon explains, on the preliminary study of 
Alkimia sptculaHva, * Deinceps de plantarum natura et animalium specialis 
scientia et maxima constituitur, scilicet de omnibus animatis praeterquam de 
homine, de quo propter nobilitatem sttam et dignitatem constituitur scientia 
propria quae dicitur medicina. Sed in ordine disciplinae prima est scientia 
animatorum praecedcntium hominem et ejus usui necessariorum, quae primo 
descendit ad omne genus agri et terrae, distinguens quatuor species agrorum, 
propter vegetabilia e terra nascentia in eis. Est enim ager in quo serunt segetes 
et legumina ; est ager consitus arboribus, ut nemus : est ager pascivus, ut prata 
et deserta ; est ager qui hortus dicitur, in quo domesticae arbores et caules et 
herfoae et radices tam nutritivae quam medicinales parantur. Haec igitur 
scientia extendit se ad perfectam considerationem omnium vegetabilium quorum 
notitia nimi§ imperfecta traditur in libro Dt Vtgetahilihus Aristotelis ; et ideo 
necessaria est scientia sufficiens de plantis et animalibus supplens defectus 
librorum communium Aristotelis vulgatorum apud Latinos, qui vocantur Dt 
Plantis et Animalibus, Sed cum agrorum cultura non potest fieri sine copia 
animaliumdomesticorum,neque utilitas agrorum, praecipueconsitorumarboribus, 
et pascuorum et desertorum, posset haberi nisi nutrirentur animalia sylvestria, 
ideo extendit se haec scientia ad plenam considerationem animalium omnium ; 
et ad honim cognitionem misit Aristoteles plura millia hominum per regiones 
mundi, et fecit illa praedara quinquaginta volumina prius memorata. Haec 
autem scientia traditur in libris Plinii, in libro Palladii De Agricultura, et in libro 
Georgicorum Virgilii non ignobili, cum expositione egregii commentatoris ejus. 
Scientia septima est de animali rationali, scilicet de homine, et praecipue de 
sanitate et infirmitate ejus ; et ideo de ejus compositione et generatione illius, 
sine quibus sanitas et infirmitas ejus non possunt intelligi nec doceri. Constat 
vero quod homo est res naturalis, et ideo scientia ejus naturalibus constituta 
erit inter naturales coroprehensa. 



SCRIPTUM PRINCIPALE. xlvii 

Our aim being to understand the conditions of his health or 
disease, we have first to examine his structure and develop- 
ment, without which health and disease cannot be understood 
or spoken of. 

Finally, to complete the whole, comes Exi>erimental science. 
It is,he says, a final judge of the assertions and reasonings put 
forth in all the foregoing sciences. More than this : it gives 
directions to those engaged in other sciences as to the construc- 
tion of instruments by which their conclusions are to be tested, 
in the same way in which a navigator instructs a shipwrightas 
to the building of a ship. Thus, for instance, it instructs the 
geometer to make a mirror such that the rays reflected from 
it shall converge in a single point. It scrutinizes every natural, 
every artificial force. It sifts the artifices of magic, as logic 
sifts the reasonings of the sophist, so as to dissipate falsehood 
and error, and leave nothing but truth remaining. 

How Bacon would have treated this part of the subject wc 
have no means of judging, other than the sixth section of the 
Opus Majus, But even the summary exposition there given is 
enough to show how large was his conception of experimental 
method, and at the same time how carefully he steered clear 
of the danger of undervaluing the mathematical or deductive 
process of discovery. So far as was possible the two should 
be pursued simultaneously and in close alliance. Euclid's 
demonstration of his first proposition would, he says, fail to 
carry complefe conviction unless visual evidence of it were 
forthcoming in the construction of the figure. And on the 
other hand, we see that his inductive investigations of the 
rainbow were controlled at every step by deductions from 
astronomy. 

With these general remarks, we may now pass to each of 
the principal divisions of the * Scriptum Principale,' which in 
the main correspond to the order foilowed in the Opus Majus. 
First comes Language, as the channel through which the 
thoughts of other men are handed down to us ; then follows 
Mathematic, embracing the four branches of the Quadrivium, 
geomctry, arithmetic, astronomy, and music. Thence we 
pass to Physic, which included the study of the propagation 



xlviii INTRODUCTION. 

of force, specially illustrated by the radiation of light and heat. 
Next comes Alkimia Speculativa, not the mere metallurgy 
of the gold-seekers, but the study of the transformation of 
matter from its simplest to its most complicated state. The 
study of living matter foUowed, ending with Medicine, the 
science dealing with the physical structure of man. Finally, 
the edifice of the sciences iscrowned by Ethic and Metaphysic. 
Of this comprehensive scheme let us see what fragments 
are forthcoming. 



IV. Bacon's Philologv. 

In urging that the comparative study of language should 
form part of the University curriculum, Bacon stood nearly 
alone. He does indeed full justice to those among his con- 
temporaries who had promoted the translation of Greek books 
into Latin ; and, first among those, to the iilustrious bishop of 
Lincoln, his forerunner and counsellor. But though Grosseteste 
had caused many books to be translated for the sake of their 
contents, it does not appear that he or any one else had 
proposed to carry the study of language, as such, beyond the 
routine of grammar presented in the Trivium ; the Latin 
accidence and syntax of Priscian or Donatus. 

What Bacon proposed was the systematic and comparative 
study of Hebrew, Arabic, and Greek, with the dialects belonging 
to each. With Hebrew went Chaldaean, and, in more distant 
relationship, Arabic : with Greek its various dialects, which 
were, he tells us, comparable to the Picard, Norman, or Bur- 
gundian dialects of French, or to the northem, southern, 
eastern, and western dialects of English. * I do not mean,* 
says Bacon, ' that every one should learn these languages as 
he leams his mother tongue, so as to be able to speak them 
as we speak English, French, and Latin ; nor again that we 
should content ourselves with being able to translate into our 
own language the Latin versions. There is an intermediate 
degree of attainment quite easy to those who have teachers. 
We should know enough to be able to understand how these 



PHILOLOGY, xHx 

languages should be rendered in Latin. The point is that 
a man should be able to read these languages, and understand 
their grammatical structure ('accidentia partium orationis/ 
Compendtum Studii^ Brewer, p. 433). 

What Bacon's linguistic attainments were cannot be pre- 
cisely decided. No woik of his, published or unpublished, 
that I am aware of, affords evidence of knowledge of Arabic. 1 
His own words in the twcnty-fifth chapter of Opus Tertium 
are scarcely decisive on the point. ' De Arabica tango locis 
suis ; sed nihil scribo Arabice, sicut Hebraee, Graece, et Latine, 
quia evidentius et facilius ostenditur propositum meum in his. 
Nam pro studio theologiae parum valet. licet pro philosophia 
multum, et pro conversione infidelium.* Some pages printed i 
for the first time in this edition show acquaintance at least 
with the Hcbrew alphabet. An elementary Greek grammar, 
in the possession of Corpus Christi CoIIege, Oxford, testifies to 
his knowledge of Greek, which indeed is sufficiently apparent 
in the present work, and still more in the ninth and following 
chapters of the Compendium Studii (Brewer, pp. 49^-519). 
This grammar is incomplete, dealing chiefly with the alphabet, 
with the Greek system of accentuation, aspiration, and 
quantity, and with the numeral system. It concludes with the 
paradigm of the verb n/7rrft). ^lts opening sentence seems to 
indicate that it formed a part of Bacon's encyclopaedic work. 
' Here begins the first book of the volume on the grammar of 
languages other than Latin. This book deals with Greek 
grammar.' * I have already,* he continues, * spoken of the ad- 
vantage to tbe Latin world of knowing. the four languages, 
Greek, Hebrew, Arabic, and Chaldaean ; and in the preface to 
this volume devoted to grammar I have explained the divisioa 
of subjects and their order. I now proceed to consider Greek 
grammar, beginning with such rudiments as boys are taught in 
Latin in order that they may read, write, and construe simple 
pas.sages, and may pass thence to points of greater difiliculty.' 

A point of interest presents itsclf as to Bacon*s pronuncia- 
tion of Greck. Much attention is given to the transliteration of 
the Greek alphabet into its Latin equivalents. The Lord's 
Prayer, the Salutation to the Virgin, and the Apostles' Creed 

VOL. I. d 



1 INTRODUCTION. 

are written out in Latin, underlined first with the Greek words 
in Roman character, and secondly with the same words in 
Greek. The second of these is here given as an example : 

Ave Maria gratiosa Dominus cum te benedicta 
Chere Maria kecharitomeni ho Kyrios meta su eulogimeni 
Xatpe Mapfa K€xapiT(Dfiivrj 6 Kvpios ficra a-ov tvkoyrnjJvrj 

tu in mulieribus et benedictus fructus ventris tui. 
sy en gynexi ke eulogimenos ho karpos tis kilias su. 
'<rv iv yvvai^ kclL evKoyrifAfvos 6 Kapirb^ TrJ9 Koikias a-ov. 

Amen. 

Amen. 

'A/utrjy. 

It is evident from the transliteration of vowels and diphthongs 
here adopted, with which may be compared pp. 75-76 of the 
Opus Majus, printed for the first time in this edition that these 
were pronounced as in niodern Greek ^ It appears also in the 
subsequent discussion on accents, that accents were considered, 
no less than quantity, in pronunciation. Bacon may not im- 
probably have learnt the language from one of the Greeks 
who had been invited into England by Grosseteste. Some 
of these, he tells us, had become permanent residents. (In 
Compend, Studii, Brewer, pp.* 495-5 14» the same subject 
is treated.) 

In urging so strongly the study of language, Bacon had two 
main purposes in view : an improved text of the Bible, and an 

^ In the Corpus Coll. Gramnar, a systematic scheme of transliteration and of 
pronunciation is also given. We leam from it that the second letter of the 
alphabet was pronounced like the modern English v; and that there was no 
single letter rendering the soand of our b, * Item ir post fi vel v, sive in eadem 
dictione, sive in diversis, dummodo sine intervallo proferantur, sonum nostri b 
habet, quem aliter non habent, ut An/iirdr, &iiKt\o¥, Similiter r post /< vet v sonat 
nostrum d, quod aliter non habent, ut uvTixpiOTiK.* AII this is in accordance 
with modem Greek pronunciation. The transliteration of the diphthongs eo; 
and cv was a matter of some difficulty owing to the confusion between u and v, 
Bacon usually renders them as d/and ef, But in modera Greek it is only before 
^. *» f I "^t ^^ '■> 0» X» ^» t^*^ t**^y ^*^ thws pronounced ; before other letters they 
would have the sound of av or ^. With regard to accents, Bacon's language 
(both in the Corpus MS. aud in the Compendiuin Siudu) puts it beyond all 
doubt that they goveraed his pronuncialion of the language. 



PHILOLOGY, li 

intelligible translation of Aristotle. Undcr both these heads 
the minor works, edited by Brewer, contain much for which in 
the Opus Majus Bacon had not found room. With regard 
to the first, the valuable memoir puHished in 18H8 by Abb^ 
Martin may be consulted ^ It appears that, towards the end 
of the twelfth or the beginning of the thirteenth century, a text 
of the Bible had become generally current in Paris under the 
title of ' Textus Parisiensis/ Bacon, writing in 1267, speaks of 
it as having been hastily compiled, about forty years before, by 
second-rate theologians and carelessly copied by uncriticai 
booksellers {Opiis Minus^ Brewer, p. 333). It abounded in 
errors and in interpolations inserted from patristic quotations, 
from liturgies, and from the works of Joscphus- Many of, 
these errors attracted notice, and attempts were made, prin- 
cipally by members of the mendicant ordcrs, to correct them. 
But these attempts, in Bacon's judgement, only resuUed in 
making the matter worse. Each critic worked independently 
and without adequate critical apparatus. Not merely did 
Franciscan differ from Dominican, but the inembers of each 
Order differed amongst themselves. Successive corrected 
versions were put forward, each worse than the preceding, 
By the middle of the century the Paris text had fallen into 
hopeless confusion ; and it had become, in Bacons judgement, 
far the lesser evil to use the uncorrected text than any of 
those which had been so uncritically amended. Of these strong 
remarks he gives many pointed illustrations, 

So devoid were these successive editors. not merely of 
linguistic knowledge, but of the critical spirit, that they seem 
to have been entirely unaware of the origin and history of thc 
Vulgate. Bacon's history of the various Biblical versions, 
ending with that of Jerome, as given in the Opus Terimm^ 
pp. 334-349, is not one of the least interesting portions of his 
work. His principal result was to show that, before Jerome's 
translation from the Hebrew, the version regarded as authen- 
tic by the Church was the Septuagint ; although theologians 
had felt themselves at liberty to correct that version from 
that of Aquila, Symmachus, and above all of Theodotion. 

* Sec note on vol. i. p. 77. 

d 2 



lii INTRODUCTION. 

After the time of Jerome, the translation from the Septuagint 
continued to be used in the Psalter; but, with that exception, 
Jerome's translatton from the Hebrew constituted the Vulgate, 
and was received as authentic by the Church. Bacon is care- 
ful to add that Jerome*s version is by no means free from 
error, due partly to over-haste, partly to his unwillingness to 
offend his contemporaries by- making too many changes in 
the text hitherto accepted. 

With Aristotle the case was even worse than with the 
Bible. The brilliant hopes with which the century had 
opened, of re-entering the temple of Greek wisdom, and 
listening to the voice of the greatest of ancient thinkers, 
had been falsified by the failure of Aristotle*s translators 
to comply with the two elementary conditions of transla- 
tion; knowledge of the language in which, and compre- 
hension of the subject about which, the book was written. 
Something has already been said of the Toledo school of 
translators instituted by Archbishop Raymond in the twelfth 
century. A new and vigorous impulse was given forty or 
fifty years afterwards by the Empjeror Frederic II, whose 
preference of Mahommedanism to Christianity, had he 
occupied a humbler station, would assuredly have subjected 
him to a worse fate than that of Bacon. Leaving out of 
account translations of Aristotle's Organum, parts of which 
were familiar to the westem world from the times of Augustine 
and Boethius, the translators of Aristotle's philosophic and 
scientific work in.the twelfth and thirteenth century, to whom 
Bacon calls attention, were five : Gerard of Cremona, Alured 
or Alfred of England, Michael Scot, Hermann the German, 
William of Moerbeke, otherwise called the Fleming. Of 
these, Gerard, Scot, and Hermann translated from Arabic 
versions. Gerard spent many years in Spain, attained a 
thorough knowledge of Arabic, and translated Ptolemy s 
Ahnagest^ and Aristotle's Meteorologics^ also thc astronomy 
of Alfraganus, several works of Alkindi, and, almost certainly, 
the Optics of Alhazen. He died in 1187. Michael Scot 
flourished in the first half of the thirteenth century. He 
was a friend of the Emperor Frederic II, under whose 



mmmm 



PHILOLOGY. liii 

patronage he visited Spain, and translated from the Arabic 
many of Aristotle's works, with the comments of Averroes. 
Albertus Magnus says of him that he was ignorant of natural 
things, and that he did not thoroughly understand Aristotle's 
books. Bacon, who speaks of the impression produced in 
the schools when he appeared in 1230, with translations of 
Aristotle*s metaphysical and scientific treatises, says that he 
was ignorant of words and of things, and that the greater 
part of his work was due to Andrew the Jew. Scot's transla- 
tion of Avicenna's treatise De Animalibus^ as I have remarked 
in a note (vol. ii. p. 85), certainly seems to bear out this 
severe judgement. Hermann, the German, was personally 
known to Bacon ; he worked in Spain, and with the help of 
Arab interpreters, produced translations of the Rhetoric, 
Poctic, and Ethic of Aristotle. He mentions incidentally 
{yourdain^ p. 140) that Grosseteste had produced a more 
complete rendering of the Ethic directly from the Greek. 
Hermann, in answer to some questions put to him by Bacon as 
to Aristotle's logical works, frankly confessed his ignorance of 
logic. ' Nor was he well acquainted,' Bacon continues, * with 
Arabic, being rather an encourager of translations than a 
translator himself; the principal part of his work was done 
by Saracens in his employment ' (Compefid, Studii^ cap, 8). 

William the Fleming (of Moerbeke) had the advant^^e 
over these men that he translated directly from the Greek. 
His work is believed to have beeh done at the special request 
of Thomas Aquinas, who made use of it in his Commentaries 
on Aristotle. ' But it was notorious in Paris,' says Bacon, • that 
William of Moerbeke was totally ignorant of science, and his 
translattons are consequently fuU of errors.' On the whole, 
he concludes that it would have been better that Aristotle 
should never have been translated, rather than that sueh 
a mass of error should be propagated under the shelter of his 
name. Had I the power of disposing of these works, I would 
have them all bumt : it is a waste of time to study them, 
a source of error and of diflTusion of ignorance greater than 
can be described.' 'AristotIe's works,' he continues, *are the 
foundation of all wisdom, but they must be studied in the 



liv INTRODUCTION. 

original to be of any profit' [Compend, Sludii, Brewer, 
p. 469). 

Every one who considers Bacon's efforts in promoting the 
study of language must agree with Professor Brewer (p. Ixii) 
that * his labours in this respect have attracted less attention 
than they deserve. . . . It is as creditable to his discernment 
as to his courage that he^should have seen, better than Lord 
Bacon did, the paramouitt importance of philology, and urged 
it repeatedly on his contemporaries. It is amazing to hear 
a scholar of the thirteenth century insisting on the necessity of 
constant references to original authorities as the only sure 
foundation of sacred criticism.' 

It may be that Bacon's exhortations, reiterated as we feel 
sure they would be, not in writing merely, but in conversation 
with the young men whom he gathered round him, were not 
entirely without effect on the following generation. In the 
council convoked in 13 12 by Clement V at Vienne, one of 
the provisions, says Fleury (Hist. EccL book 9 1 ), was ' the 
estabhshment in the Roman Curia, and in the Universities of 
Paris, Oxford, Bologna, and Salamanca, of teachers for the 
three languages, Hebrew, Arabic, and Chaldaean, two for 
each. They were to be maintained in Rome by the Pope, in 
Paris by the King of France, and in the other cities by the 
prelates, bishops, and chapters of the country.' This subject 
has been carefully studied by Mr. Rashdall in his important 
work on the Universities of Europe in the middle ages. He 
gives strong authority for the belief that Greek was included ; 
and if so, the avowed purpose of the ordinance, which was 
the conversion of the Mahommedans and Jews, may not have 
been the only purpose ; some faint echo of Bacon*s exhorta- 
tion to study Aristotle and the Bible in the original, with the 
view of understanding them better, may have been still audible. 
Few and short-lived were the attempts made to carry the 
decree of this Council into effect. In 1320 we hear of a rate 
levied upon benefices in the province of Canterbury for the 
support of a converted Jew alleged to be teaching Greek at 
Oxford. But Oxford was already passing under the spell of 
the enchanter. The fine webs of Duns Scotus, which the 



MATHEMATICS. Iv 

sword of Ockham might cleave but could not dissipate, were 
paralyzing her energies. Five generations were to pass before 
she could again begin to promote the study of *lang^ages 
other than Latin ^ * ; and even then not in the comprehensive 
spirit which Bacon had advocated. It is tempting, though 
painful and perhaps useless, to imagine how far European 
culture might have advanced had schoolsof Oriental lang^ages, 
conairrently with those of Greek and Latin, bcen instituted 
and continuously maintained from the thirteenth century. 

V. Bacon's Mathematics. 

In the Optis Majus, though much is said of the importance 
and necessity of mathematical method, there is very little 
display of mathematical knowledge. Frequent references are 
made to Euclid, whose Elements had been introduced to the 
westem world early in the previous century, by Adelard of 
Bath, and more completely in the thirteenth century by Cam- 
panus of Novara. Archimedes and Apollonius are rarely 
mentioned. But in his Optics Bacon shows that he was 
acquainted with the properties of parabolic concave mirrors. 
and of their power of causing parallel rays to converge after 
reflection to a focus. In this respect he was in advance of his 
principal teachers in Optic, Euclid, Ptolemy, and Alhazen. 

Of the Calculus, arithmetical or algebraical, Bacon has but 
sltght occasion to speak in the Opus Majus. It has always 
to be remembered that this work, with its appendices, the 
Opus Minus and Opus Tertium^ was not, properly speaking, 
a philosophical treatise^ but an exhortation addressed to a 
statesman, absorbed in ecclesiastical and political struggles, 
to exert his authority for the revival of learning. Hence it 
is uniformly spoken of as a Persuasio, It contains just as 
much learning and science as was thought needful to convincc 
the Pope that learning and science were capable of strengthen- 
ing the Church. It is but the preamble to the *Scriptum 

^ Tbe organized teaching: of Greek in Oxford is due to Richard Foxe, the 
founder of Corpus Christi College (1515-16;. But when Erasmus was in Oxford 
about twenty years earlier, such men as Thomas Linacre and William Grocyn 
had already become Greek scholars, under the teaching, perhaps, of Comelio 
VHelU. (Cf. Hallam, Lit. Hisi, ofEuropt, part i. ch. 3.) 



Ivi INTRODUCTION. 

Principale,' which there is reason for thinking that Bacon 
had already begun, but which he regretfully expresses his 
inability to send at such short notice. Hence though it deals, 
often very cursorily, with every department of knowledge 
then recognized, we must not infer Bacons ignorance of 
a subject from the fact that this provisional treatise makes 
no mention of it, 

Among the fragments of the * Scriptum Principale ' which 
have come down to us, is a portion of the first book on 
Mathematics, preserved among the Sloane MSS. (2156). This 
first book contained three parts. We have the first part of 
this book, and a considerable part of the second. A few 
fragments more are to be found in the Bodleian (Digby MSS. 
76). As far as I am aware nothing more is extant. 

The first part deals with preliminary principles (' quaedam 
preambula ad interiora mathematicae '). 

It has five divisions or distinctions. The subjects dealt 
with are the relation of mathematic to metaphysic : its dis- 
tinction from magic; the hindrances to its culture oflfered by 
the four causes of error, viz. false conceit of wisdom, authority, 
custom, and popular prejudice ; the utility of mathematics, its 
importance to the preliminary studies of logic and grammar. 
The final chapter of this section is curious. The final purpose, 
says Bacon, of logic is conviction. But conviction is not 
reached by argumentative process alone, but by the arts of 
rhetoric and poetry, which are therefore in a true sense 
departments of logic. But the>e arts are govemed by the 
laws of music, which is a branch of mathematical science. 

The second division deals with the definition of the parts 
of quantity. Certain general terms, such as simultaneity in 
space and time, limit, continuity, infinity, dimension, are 
explained. The distinction is drawn between continuous and 
discrete quantity. Continuous quantity in one, two, and three 
dimensions is defined. Discrete quantity is distinguished into 
what is permanent, as number; what is not permanent, as 
sound. 

The third division expounds the distinction between the 
speculative and the practical departments of geometry and 



MATHEMATICS. Ivii 

of arithmetic. The section on practical or applied geometry 
is of much interest as illustrating Bacon's enlarged views of 
scientific training. He indicates eight departments of this 
branch of sciencc. (i) Agriculture, in a far wider sense than 
is usually given to the word, comprising mensuration, archi- 
tecture, civil, mechanical, and military engineering. (2) The 
fabrication of astronomical instruments. (3) Of musical in- 
struments. (4) Of optical instruments. (5) Of barological 
instruments. (6) Of instruments of experimental science. 
(7) Of medical and surgical appliances. (8) Of chemical 
apparatus. 

In connexion with the practical branch of arithmetic, after 
speaking of the use of the Abacus, he mentions * vias algorithmi, 
scilicet quomodo conjugantur numeri et dividuntur,secundum 
omnem speciem algorithmi, tam in particularibus fractionibus 
quam in integris.* In this connexion he speaks of *Algebra 
quae est negotiatio, et almochabala quae est census.' How 
far Bacon had assimilated the work of Mohammed ben Musa^, 
whose surname, AI Chwarismi, is incorporated in the word 
Algorithm, we cannot tell. But with the work of one of the 
two great mathematicians of the thirteenth century, Jordanus 
Nemorarius, hc was certainly familiar, as may be seen by 
reference to vol. i. pp. 158, 169 of the Opiis Majiis, Among 
other branches of practical arithmetic he includes the con- 
struction of astronomical tables, mensuration, alloys and 
coinage, partnership, and other operations of commerce. 
Thcse things are treated of at great length in the Liber 
Abaci of Leonard of Pisa, the other great mathematician 
of the timc, whose work, dedicated to Michael Scot, Bacon 

* Muhammed ibn MOsii Alchwarismi was bom in the first quarter of the ninth 
centuiy. Hc constnicted astronomical tables for the Caliph Al Mamoun, which 
were translated into Latin by Adelard of Bath. Of more importance, however, 
are his Arithmetic and his Algebra. The first of these remained for a long time 
unknown. But it was discovered in Cambridge in 1857, and is included among 
the TrmtUtH dAritmtiica published by Boncompagni. A full account of this 
work and of the Algebra, tmnslated and edited by Rosen (^London, 1831), will 
bc found in Cantor, vol. L pp. 611-629. Cantor [j>. 619) explains clearly the 
passage of the word Alchwarismi into Algorithm. Bacon's interpretation of the 
words Aldschebr walmukAbala» which Alchwarismi uses, is incorrect. Dschebr 
means Restoration, muVAbala means opposition. 



Iviii INTRODUCTION. 

had possibly seen and studied ; though he makes no mention 
of it, in any work known to us '. 

Astrology and astronomy come next The first is the 
speculative branch, dealing with planetary motions, with the 
figure of the earth and of its various regions. Astronomy, 
the practical branch, has to do with the construction of tables 
and with the forecast of future events. Bacon admits that this 
use of the words has not been universally adopted, but main- 
tains its correctness. * Astrologia componitur ex hoc nomine 
astron quod est stella, et hoc nomine logos quod est verbum, 
vel ratio> vel sermo. quia est sermo de stellis. Astronomia vero 
dicitur lex steliarum et nomos est lex. Unde quia lex univer- 
saliter sonat in practicum, ut in morali philosophia lex estipsa 
practica, ita similiter Astronomia est practica astronomiae.* 

In the fourth division music is considered. This includes 
not merely sound but gesture. Audible music is considered 
under the two heads of vocal and instrumental. In the vocal 
division every branch of elocution is included. Finally, the 
effect of music on the temper and health both of men and of 
animals should be systematically studied. 

Abstraction is the subject of the fifth division. First we 
have the abstraction common to all science, since science 
deals with universals, not with particulars. There is then the 
abstraction of a first cause from secondary causes and of spirit 
from body, which the metaphysician deals with. Mathematical 
abstraction has to do with the study of quantity apart froni 
the substance to which it belongs: apart from all natural 
changes such as growth, diminution or change of place. 

This first part closes with an explanation of the difference 
between axioms, postulates, and definitions. 

The second part begins with the study of whole numbers 
and fractions : passing from this to the subject of arithmetical, 
geometrical, and harmonic ratio, and to Ihe question of pro- 
portion generally. Continuous and discontinuous proportion 
are considered ; and Euclid's definition of proportion is care- 
fully considered. 

' To each of these two mathematicians Cantor devotes a fuU chapter. Cf. 
Gtsch, der Math, vol. ii. pp. 3-79. 



ASTROLOGY. lix 

Here the portion of the work contained in the Sloane MSS. 
ends. We find it continued, however, in a somewhat frag- 
mentary way in the Bodleian Digby MSS. No. 76. The 
author proceeds to the consideration of geometrical truths, 
professing his intention to select those which were of para- 
mount importance, since it was obvious that the number of 
possible problems in geometry was infinite. 

'IUae (veritates),* he says, 'sunt eligendae quae possunt 
vocari radices et elementa respectu ramorum et foliorum, 
quorum fructus vadit in infinitum/ Proof is given in this 
part of the work that Bacon was acquainted with the geometry 
of Apollonius as well as with that of Euclid. After defining 
the cone (* pyramis rotunda')he mentions its three sections, 
presenting curves of a different form from the circle, one of 
which was of use in the construction of mirrors capable of 
rendering rays convergent to a point. He promises to deal 
with these curves later in the work. 

Of the whole, so far as the fragment of his mathematical 
work preserved to us enables us to judge, it would seem that 
Bacon had made himself acquainted with the highest mathe- 
matics of his time ; though no evidence is forthcoming to show 
that he contributed personally to the advance of the scicnce, 
otherwise than by strongly insisting on its culture, and by 
pointing out new fields for its practical application, in the 
better government of the Church, and in the development of 
industry. His interest, like that of Galileo, lay in applied 
rather than in abstract mathematics. Whether the study of 
equations as carried on by the Italian algebraists of the 
fourteenth and fifteenth centuries would have interested 
him is doubtful. But he would have eagerly welcomed the 
invention of logarithms, as facilitating the construction of 
astronomical tables. 

VI. Bacon's Astrology. 

The transition from Mathematics to Physics supplies the 
best opportunity for a few remarks on the subject of Bacon's 
Astrology, on which something is also said in a note to vol. i. 
p. 269. Bacon dwclt frequently and cmphatically on the 



Ix INTRODUCTION. 

unity and the correlation of the sciences. In passing from 
Mathematics to the direct study of Nature, he found a con- 
necting link in the imaginary science of Astrology, which 
he studied zealously. That the iixed stars and the planets 
exercised a powerful influence on all earthly things and not 
least on man ; that the careful observation of their position ^ 
at the moment of birth would do much to reveal the hidden 
springs of character, and make it possible to form a forecast 
of the ensuing life, that the influences radiating from them 
acted with greater or less potency according as the course of 
the rays was perpendicular or oblique, and that in this way 
an explanation could be given of climate, temperament, and 
of the thousand complex chances and changes of mortal life, 
was a belief firmly held by Bacon, and it operated povverfuUy 
over his whole view of mans position in the world. He has 
been much reproached for holding it ; and it has been supposed 
to be an explanation, if not an excusc, for the disastrous 
repression exercised over him by his superiors, and for the 
popular discredit attaching to his namc. 

But this would be an entire misconception of the beliefs 
current in Bacon's time. The influence of the stars over 
human life was a belief almost universally hcld by all instructed 
men from the thirteenth to the sixteenth century ; and 
abundant traces of it are.visible throughout the seventeenth, 
not to speak of still later times. The Divina Commedia is full 
of it. Beatrice, admonishing Dante at her first meeting with 
him in the Earthly Paradise, speaks of the rich endowment 
with which he came into the world, 

*Per ovra delle ruote magne, 
Che drizzan ciascun seme ad alcun fine, 
Secondo che le stelle son compagne*.* 

* PurgaU XXX. 109-11. Even more significant is thc passage, Parad.\\\\. 
127-33 : — 

' La circular natura, ch' h suggello 
Alla cera mortal, fa ben sua arte 
Ma non distingue Tun dall' altro ostello. 
Quinci addivien ch' Esau si diparte 
Per seme da Jac6b, e vien Quinno 
Da si vil padre che si rende a Marte/ 



ASTROLOCY. Ixi 

By Dante's master in theology, Thomas Aquinas, the reality 
of astrological influences is latd down with perfect cleamess 
ia 5. T. Pars Prima (quaest* 115, art. 3 and 4). In thc 
first instance the question is put whether heavenly bodies are 
a cause of things that take place in terrestrial bodies. This 
after the usual statement of reasons, for and against, is answered 
emphatically in the affirmative. *Celestial bodies causally 
affect all the varied motions of terrestrial bodies^* The second 
question is, Are heavenly bodies a cause of human actions ? 
The authoritative conclusion here is, Directly speaking, they 
are not, but indirectly they arc^ * Indirectly, and by accident, 
impressions of celestial bodies may reach intellect and will, 
since both intellect and will receive somewhat from inferior 
faculties which are bound up with bodily organs. A disr 
tinction is, however, to be made between will and intellect. 
The intellect is of necessity affected by the lower apprehen- 
sive faculties of imagination. thought, or memory, and when 
these are stirred, the intellect is stirred likewise. But the 
will does not of necessity follow the promptings of the 
iower appetite. For although the passions of anger and 
desire have a certain power of moving the will ; yet it 
rcmains in the power of will to follow passion or to repu- 
diate it Thus the influence of celestial bodies, so far as 
it produces change in the lower faculties, has to do rather 
with intellect than with will ; and will is the proximatc cause 
of human action.' 

Finally Aquinas remarks that * most men follow passions, 
which are motions of the sensitive appetite ; and with these 
heavenly bodies may have to do. For few are the wise who 
withstand such passions. And thus it is that astrologers 
may often foretcU truly; but for the most part rather in 
general than in special, since nothing hinders any one man 

* The words are: 'Corpora caelestia cum tantum mobilia sint secundum 
lationis motum, causa sunt omniQm eorum quae in his corporibus inferioribus 
variis motibus aguntur.* 

' 'Cum intellectus et voluntas, quae humanorum actuum principia sunt, 
corporeis organis vires alligatae minimc sint ; non possunt corpora ipsa caelestia 
hunianonim actuum causae directe esse, sed indirecte, agendo per se in corpora 
que ad utriusque potentiae opera conducunt.' 



Ixii INTRODUCTION 

from withstanding passions by free will. Hence, astrologers 
themselves say that the wise man governs the stars, in so far, 
namely, as he governs his own passions/ Further on, in 
Prima Secuudae^ quaest. ix. art. 5, this subject is again dis- 
cussed. The question asked is, *Can will be influenced by 
a heavenly body ? ' The conclusion is, ' Since will is a faculty 
absoluteiy immaterial and incorporeal, it can only be in- 
fluenced by heavenly bodies indirectly.* And in his comment 
Aquinas observes, * So far as will is influenced by any out- 
ward object, it can evidently be influenced by heavenly 
bodies : since all external bodies, which, when presented to 
the senses, move will, and even the very organs of sensitive 
faculties, are influenced by the motions of the heavens. But 
there is no direct action of heavenly bodies upon the will. 
For the will, as Aristotle says [De Anima^ lib. iii) resides in 
reason ; and reason is a power of the soul not bound to 
a bodily organ. . . . On the other hand. he adds, ^ Sensitive 
appetite is the function (actus) of a bodily organ. Wherefore 
nothing hinders impressions of celestial bodies from rendering 
some men apt to anger, or to lust, or to some passion of this 
kind; and thus from natural complexion many men foUow 
passions, and wise men alone withstand them. And so, in 
a general way, are verified those things that are foretold of 
the actions of men in accordance with the consideration 
of heavenly bodies.' 

Now the view taken by Bacon coincides precisely with that 
of Aquinas. Confusion, he says {Opus Majus, p. 150), had 
arisen in the matter in consequence of the equivocal meaning 
of the word, Mathematics, sometimes held to be derived from 
\ija,vjiKf\y sometimes from fiiOriais. The characteristic, he says, 
of false mathematic, was to assert that through the powers of 
the constellations all things took place of necessity. No place 
was left for contingent matter, for judgement, for free will. 
Such a view of nature was condemned not only by theologians 
but by philosophers. Aristotle and Plato, Cicero and Pliny. 
Avicenna and Albumazar were unanimous in holding that 
free will remained uncoerced by the motions of heavenly 
bodies. ^ True mathematicians and astrologers lay down no 



ASTROLOGY. Ixiii 

necessity, no infallibility, in their predictions of contingent 
events. . . . What they do is to consider the way in which the 
body may be affected by celestial things, and the way in 
which the body may act upon the mind in private affairs or 
public, always ^ithout prejudice to the freedom of the will. 
For although the reasonable soul is not coerced to any future 
actions, yet it may be strongly stirred and induced, so as 
freely to will those things towards which celestial force may 
incline it ; as. ^e see men in community taking counsel, or 
through fear or love, and feelings of this kind, freely choosing 
what before they would not, though not forced to do so ; like 
the sailor who to save himself from drowning throws precious 
merchandise into the sea. We see, indeed, that impressions 
from things on earth may so act upon sense as to stir men to 
will what before they had no care for, so that they take no 
account of death or disgrace or fear, if only they accomplish 
their desire, as with those who see and hear the onset of their 
enemies, and are borne onwards at all hazards to avenge them- 
selves. Far more potent than the impressions of earthly 
things are those of the heavenly upon bodily organs, which 
being strongly moved, men are led on to actions of which they 
had not thought before, yet always with fuU reservation of 
the freedom of the will.* 

There are perhaps few fictitious creeds for the origin of 
which it is so easy to account as for the belief that the position 
of the planets with regard to onc another and to the constella- 
tions of the zodiac were of significance to man and his 
environment. With populations whose religion was astrolatric 
rather than polytheistic, taking shape in worship of the heavens 
rather in that of invisible but manlike gods, astrology would 
be an easy and almost inevitable deduction from their creed. 
The immense majority of the Asiatic population, whether 
Semitic or Mongol, were, unlike the Indians and the Greeks, 
not polytheists but astrolaters. When the Arabs received 
and enlarged their inheritance of Ptolemaic astronomy, their 
astrologic beliefs, far from being dissipated, were strongly 
confirmed. Of the seven wanderers of the sky, the influence 
on earthly things of two, the Sun and the Moon, was too 



Ixiv INTRODUCTION. 

obvious to be disputed. The one swayed the tides, the other 
brought sumnier and wintcr. Why should the rest be sup- 
posed inert? Was it not probabie that the successive and 
infinitely varying connexion of each of them, singly or com- 
bined, with the fixed groups of the starry vault, indicated 
changes or tendencies to change here below which careful and 
prolonged study might at last interpret? 

So it was that with the growth of knowledge, and with 
increasing strength of the conviction that all nature was under 
the dominion of fixed laws, astrology came to be regarded as 
the key to the understanding of all that was specially con- 
tingent and variable in man's environment ; the phenomena 
of temperament and of disease ; the revolutions of states, and 
even of religions* The boundary of its lawful application was 
drawn difierently by different thinkers. Apart from charlatans 
and miracle-mongers, fcw stretched it farther than Bacon. 
But by him, as strictly as by Aquinas, the saving clause, * salva 
arbitrii libertate,* was always added. Outside influences 
might suggest motive and kindle passion ; they could never 
trench upon the sacred domain of the freedom of the will \ 

What is strange is not that the belief in the convergence of 

* Comte has pointed out {PhUosophie PosiHve, vol. iii. pp. 273-280, ed. Littrd) 
that in order to appreciate astrology with any approach to justice, it is needful 
to keep steadily in view the very real connexion between the sciences of 
astronomy and biology. On the relations of mass and of distancc between 
the sun and earth, involving as thcy do the familiar facts of weight, equilibrium 
of fluids, temperature, life on our planet is obviously dependent. If we consider 
the period and velocily of the earth's rotation, the degree of ellipticity of her 
orbit, the angle at which the axis of rotation is inclined to the plane of the orbit, 
the same truth is impressed upon us even more strongly. ' In the early stages 
of the human mind these connecting links between astronomy and biology were 
studied from a very different point of vicw ; but at least they were studied and not 
left out of sight, as is the common tendency in our own time under the restricting 
influence of a nascent and incomplete positivism. Beneath the chimerical beliefs 
of the old philosophy inthe physiological influence of the stars, therelay a strong 
though confused recognition of the truth that the facts of life were in some way 
dcpendent on the solar system. Like all primitive inspirations of man's inlelli- 
gence this feeliug needed rectiflcation by positive science, but not destruction ; 
though unhappily in science, as in politics, it is oilen hard to reorganize without 
some brief period of overthrow.' Tbis was written in 1836. Much has beea 
donc since by Mr. Spencer and others to familiarize the European mind with 
the dependence of life on its astronomical conditions. But the injustice in our 
historical judgement of mcdiaeval astrology still remains. 



PROPAGATION OF FORCE Ixv 

stellar influences towards thc central point of a closed universe 
should have arisen, but that it should so long and so per- 
sistentlyhave survived the discovery that the universewas not 
closed but boundless. That Francis Bacon, who rcjected or 
doubted the Copemican theory, should have retained his beiief 
in astrology is not surprising. But we should have expected 
that with men like Kepler and Campanella, it would have 
vanished like the moming mist. Yet it was not so. 



VII. The Propagation of Force. 

Bacon's views of stellar influences must be taken in con- 
nexion with his speculations as to the transmissions of force 
through space. These are set forth briefly in the second and 
third Distinctions of the fourth part of the Opus Majus ; and 
more in detail in the special treatise De Multiplicatione 
Specierum^ which in this edition is given as an appendix. 

*Species' is the word chosen by Bacon to express the 
emanation of force which he conceives to be continually pro- 
ceeding from every bodily object in all directions. Body of 
cvery kind is endowed with force which indeed is identical 
with its substance or essence. The first result of this force, 
resembling it in character, is its species, otherwise called 
likeness, or image, or intention or impression In othcr 
words, body is a centre of activity or force radiating in every 
direction. Species is the first result of this force, the ray 
proceeding from the body. Tracing back this doctrine to its 
origin, we find it expounded in the fourth book of Lucretius, 
in Diogenes Laertius' account of the system of Epicurus, and 
in the traces that remain to us of older philosophers, notably 
of Democritus. Aristotle, in his short treatise on Divination 
by dreams, alludes to the theory of Democl^itus that ctdoiAa • 
and avoppoiai were continually emitted from objects which in 
the stillness of the night were capable of affecting the sleeper. 
By Epicums, in his letter to Herodotus quoted in his biography 
by Diogenes Laertius, the theory is more fully detailed. ' There 
are. moulds,' he says, * corresponding to all solid bodies pre- 
serving the same shape and arrangement as these bodies 

VOL. I. e 



Ixvi INTRODUCTION. 

which emanate from them, and are conveyed through space 
with incredible velocity. These may be called images. Their 
flow from bodies is continuous so that they are not separately 
perceived.* The description of them by Lucretius is more 
definite and better known. ^Pictures of things and thin 
shapes are emitted from things off their surface; these are 
like films or may each be named a rind, because each image 
bears an appearance and form like to the thing, whatever it is, 
from whose body it is shed and wanders forth ' (Lucretius 
iv. 40, Monro's translation). And again, * Many idols are be- 
gotten in a short time, so that the birth of such things is with 
good reason named a rapid one. And as the sun must send 
forth many rays of h*ght in a short time in order that all things 
may be continually filled with it, so also for a like reason 
there must be carried away from things in a moment of time 
idols of things, many in number, in many ways, in all directions 
round. . . . As soon as ever the brightness of water is set down 
in the open air, if the heaven is starry, in a moment the clear 
radiant constellations of aether imaged in the water correspond 
to those in the heaven. Now do you see in what a moment 
of time an image drops down from the borders of heaven to 
the borders of earth ' (Lucretius iv. 159 and ai 1). He goes on 
to explain that not the sense of si^ht only, but all the senses, 
are affected by these emanations. 

But it would be an entire misapprehension of Bacon's views 
as to the propagation of force to identify them with the crude 
physics of Epicurus. 

In the first place, Bacon wholly rejects the notion that the 
species is something emitted from the agent, or acting body 
(De Mult, Spec, pp. 432-438). If it were so, the agent would 
be weakened and ultimately destroycd by the emission, which 
is not the case. Nor again does the agent create the species 
out of nothing. Nor does it collect the species from sur- 
rounding space and send it on into the body on which action 
takcs place — the patient. Nor, as some have supposed, does 
the agent impress the patient as with a seal. 

What happens is that the agent stimulates the potential 
activity of the matter of the patient. The species is generated 



PROPAGATION OF FORCE. IxvH 

out of the matter acted on. * Fit species de potentia activa 
materiae patientis.' The agent acts on the first part of the 
body of the patient, and stimulates its latent energy to the 
generation of the species. That part thus transmuted acts on 
the part next succeeding ; and so the action proceeds {DeMult, 
Spec, p. 457). 

While the agent acts on the patient, the patient re-acts on 
the agent. ' Omne agens physice patitur et transmutatur 
insimul dum agit, et omne patiens physice agit ' {De MulL 
Spec, p. 439). Heavenly bodies as they act on one another, so 
do they receive emanations of force from terrestrial bodies. 
Not that they are so affected by them as to be destroyed, 
being incorruptible. Nevertheless there is in this way an 
interchange of force between all parts of the universe (p. 448). 

The ray, or species, is of corporeal nature ; but this corporeal 
nature is not distinct from that of the medium ; it is generated 
from the substance of the medium, and is continually re-formed 
out of successive portions of the medium occurring in the line 
along which the force is propagated (p. 505). If wind is 
driving the air transversely to the line of force, this in no way 
affects this line. The species is formed and reformed from 
particles of the medium presented in the line of propagation, 
and from no others. 

Finally the propagation of rays occupies time (vol. ii. pp. 
67-72 and 525-9), though its velocity is such that the time 
occupied in passing through so vast a space as the diameter 
of the universe is imperceptible to sense. 

It will be seen from the foregoing how wide is the divergence 
between Democritean and Baconian physics. Though Bacon 
retains the word ' species ' in his theory, the word has almost 
entirely lost the significance attached to it by Lucretius. 
We are no longer dealing with the notion that bodies emit 
from their surface films or moulds which are transmitted 
through space. Like the word * ray,' which is retained by the 
modem physicist who accepts the undulatory thcory, * species ' 
for Bacon has become a mere word to denote the propagation 
of force in certain definite directions. Indeed the multiplica- 
tion of species as defined by him has much in common with 

e 2 



Ixviii INTRODUCTION. 

the undulatory theory. He formally rejects the contrasted 
theory of emission. The species, like the wave, is a motion 
or change in successive portions of the aerial or ethereal 
medium ; occupying time in its transit : propagated so long 
as the medium be homogeneous, in direct h"nes ; liable to 
deflection when the medium alters its character. 

In Bacon's theory of the radiation of forces two very 
important points are to be noted. The first is his clear grasp 
of the principle that time was occupied in their transmissiori. 
He discusses, in the passages already cited, the view of Aristotle 
and others that the propagation of light differed from that of 
sound and odour by being instantaneous. We might admit, 
Aristotle had said, that light could pass through short spaces 
without our being able to detect any interval of time during 
the passage. But when light passes from east to west through 
the universe, the space is so vast that if time were occupied 
we could not fail to detect it. Bacon's conception of the 
subject is far more scientific. Our inability to perceive minute 
intervals of time is no evidence, he said, for their non-existence. 
Imperceptible time, he remarks, has many degrees. There 
is, first, the interval of time occupied by a single propagation 
of force (or, as we should say, undulation) foUowed by the 
interval of rest before the next propagation begins. Take 
such a multiple of that interval as would suflRce for the whole 
distance between the extremities of a diameter of the universe, 
and that multiple may still remain below the limits of our 
power of perception. It is interesting to compare with this 
passage the speculations of the second Bacon on the same 
subject {Nav. Org. ii. 46). Francis Bacon had formed the 
conjecture that the transit of light from the stars occupied 
time. But he did not grasp this conjecture with the same 
firmness as Roger Bacon, and he follows it up with ingenious 
arguments which explain it away. 

Radiant force, in Bacon*s view, proceeded independently of 
man's power to perceive it. Opaque bodies, he observes, 
offered resistance to the passage of a luminous ray {De Mult. 
Spec, p. 47^ ; see also vol. i. p. 114). But * no substance is so 
dense as altogether to prevent rays from passing. Matter 



OPTICS. Ixix 

18 common to all things, and thus there is no substance on 
which the action- involved in the passage of a ray may not 
produce a change. Thus it is that rays of heat and sound 
penetrate through the walls of a vessel of gold or brass. It 
is said by Boetius that a lynx*s eye will pierce through thick 
walls. In this case the wali would be permeable to visual 
rays. In any case there are many dense bodies which 
akogether interfere with the visual and other senses of man, 
so that rays cannot pass with such energy as to produce an 
effect on human sense, and yet nevertheless rays do really 
pass, though without our being aware of it.\ Recent dis- 
coveries have given significance to this remarkable passage ; 
which, not merely to his contemporaries but to succeeding 
generations, must have seemed in the highest degree fan- 
tastical. 

VIII. Bacon's Optics. 

The most striking illustration of laws governing the transit 
of force through space was obviously to be looked for in the 
science of Optics {Perspectiva). The fifth section of the Opus 
MajuSy amounting to about one-fifth of the whoie, is devoted 
to this sdence ; and much supplemental matter is added in 
the treatise De Multiplicatione Specierum. Optics had been 
studied by the Greeks to much purpose. The works of Euciid, 
Theon, and Ptolemy were translated into Arabic, and were 
carefully studied by Arabian men of science, notably by AbQ 
'Ai! al Hasan ibn al Hasan ibn Alhaitam, better known to 
Occidentals under the name of Alhazen. Their principal 
results are embodied in Bacon's work. 

Euclid, or the author passing under his name^ was aware 
that light proceeded in straight lines, and that visual rays were 
rcflected from plane mirrors in such a way that the angles 

' Heibeng, in his recent edition of £udid's Optica\ioTXD\ti% the seventh volume 
of the complete edition of Euclid, edited by Heiberg and Menge), remarks 
'p. xxviii of ProUgomina\ * Optica qualia hic e codice Vindobonensi maxime 
primo loco repetivimus, Euclidis esse, non est cur dubitemus. Sed cum recen- 
tiores tantum extent codices, minim non est locos nonnuUos tam corruptos 
esse ut verba Eudidis restitui nequeant.' 



Ixx INTRODUCTION, 

made with the surface on each side were equal. He con- 
ceived the assemblage of rays as a cone having its apex in the 
eye, and its base in the boundary of the object seen : that the 
apparent magnitude of the object depended on the magnitude 
of the angle of the cone. Thence followed the ordinary prin- 
ciples of perspective, as that of equal magnitudes at unequal 
distances ; those nearer to the eye appeared larger, and so on. 
In the Catoptrica (attributed to Euclid, but probably due to 
Theon), from the equality of the angles of reflexion and inci- 
dence in plane mirrors was deduced the convergence of rays 
faUing on a concave specuium. 

Ptolemy ^ carried the science much further than Euclid. To 
the study of reflected light he added that of refraction. The 
chief interest of his work lies in the application to the subject 
of the experimental method, an instance of it unique, if we ex- 
cept the Pythagorean experiments in acoustics, in the history 
of Greek science. Using an extremely simple but ingenious 
apparatus, he discovered, not merely that the luminous 
ray in passing from one medium to another was deflected, 
but, within certain limits, he ascertained the amount of de- 
flexion and its dependence on two distinct factors, the angle 
of incidence, and the nature of the two media concemed. 
Ptolemy distinctly describes and explains the error introduced 
by refraction into astronomical observations. The fact that 
in his great astronomical treatise there is no mention of refrac- 
tion had led to the conclusion that the Almagest and the 
Optics must be attributed to distinct authors. The Optics, 
however, may be a later work. We know it only from a trans- 
lation from the Arabic into Latin, made in the twelfth century ; 
it has been recently edited by Gilberto Govi, of Turin. The 
researches of Euclid, Ptolemy, and others on Optics, engaged 
the attention of the Arabian schools from an early period. 

* On Ptolemy's OpHcs Uiere is a very interesting chapter in Delambre*8 
AsironomU Ancienne^ vol. ii. pp. 411-430, ed. 1817. (See also a note on p. li of 
Prcface to vol. i which modifies some of his conclusions.) AII our knowledge 
of Ptolemy*s optical work comes from an imperfect Latin translation from the 
Arabic made in the twelflh century by Admiral Eugenius of Sicily. There are 
late MSS. of this work in Paris and in the Bodleian Library. But Govi*s 
recent edition is from a much older MS. in the Ambrosian Library of Milan. 



OPTICS. Ixxi 

Their knowledge of the subject is summed up in the work of 
Alhazen, whose remarkable work, Thesaurus Opticae, written 
perhaps in the eleventh century, was translated in the twelfth 
into Latin ; as Jourdain thinks, by Gerard of Cremona, the 
translator of Ptolemy's AlmagesL Alhazen was the writer on 
whom Roger Bacon principally relied ; though he makes fre- 
quent use of the opticai treatises of Euclid, Ptolemy, Tideus, 
and Alkindi. 

Alhazen*s work is copious in the extreme ; in some parts 
extremely tedious. Its value as a document in the history of 
science is, however, very great. It consists of seven books. 
The first begins with a brief exposition of the nature of light 
and colour, and proceeds to explain the anatomy of the organs 
of vision. The second deals with the function of vision and 
with the physiology of perception. The third, with imper- 
fections and illusions incident to vision. The fourth, fifth. and 
sixth are devoted to the subject of reflexion. Seven kinds of 
mirrors are discussed, plane, spherical, cylindrical, and conical ; 
the convex and concave forms of the three last being separately 
constdered. The multiplication and position of theimages 
formed is treated with inordinate length, but with such 
geometrical skill as to secure for him an abiding place in the 
history of pure, no less than of applied mathematics. ' His 
investigation,' says Cantor {Geschichte der Mathematiky vol. i. 
p. 677), * of the problem : In a spherical concave mirror, to find 
the point from which an object of given position will be 
reflected to an eye of given position, is one which, analytically 
handled, leads to an equation of the fourth degree.' Alhazen 
solved it, as Govi remarks (Ptol. Opt. p. xix), by the use of 
an hyperbola. 

The seventh book of the Thesaurus Opticae deals with re- 
fraction. A very elaborate description is given of the instru- 
ment for measuring it, part of which Bacon quotes. Moreover, 
an attempt is made to explain the cause of refraction which is 
substantially identical with Bacon's, as may be seen by com- 
parison of Alhazen vii. 8 with De Mult, Specierum^ Part II. 
cap. 3. The apparatus for measuring the angle of refraclion, 
which was more accurately designed than that of Ptolemy, 



Ixxii INTRODUCTION. 

enabled a series of observations to be made of the angle of 
refraction, in different media, on which the true law of the 
variations of refraction at different angles and in different 
media might ultimately be based. Vitello ^ Bacon's contem- 
porary, drew up a table of refractions, as Ptolemy had done 
before him, for the three media of air, water, and glass. It 
was soon seen that the angle of refraction did not vary in 
accordance with the angle of incidence. But more than three 
centuries were to pass before the discovery of the law of 
sines, that is to say, the law that the ratio of the sines 
of the angles of incidence and refraction is constant for 
refraction in the same medium, was effected by Snell and 
Descartes. 

It might seem, at first sight, that the optical work of Bacon 
was little more than an abridgement of that of Alhazen ^. But 
this view would render Bacon but scanty justice. Problems 
of great importance were indicated by him which Alhazen had 
entirely neglected. In considering the point on the axis of 
a spherical concave mirror to which rays were reflected, Bacon 
remarks that this point would be different for rays reflected 
from each concentric circle traced round the centre of the 
mirror. Such a mirror failed therefore to produce complete 

* Of Vitcllo, or Witelo, very little is known. He describes himself in his 
dedication to William of Morbeta (identified by Cantor as William of 
Moerbeke) as iilius Thuringorum et Polonorum. In lib. x. 74 of his work he 
speaks of Poland as his country, and other passages (x. 42 and 67) show 
that he travelled in Italy. His work on Optics was edited with great care, and 
with many cmendations, by Risner, and published at Bale in 1579 in the 
same volume that contained Risner's edition of Alhazen. Indeed, it may 
be described with little exaggeration as a revised edition of AIhazen's work ; 
with many additions certainly from other authors, but with noue of those 
acknowledgements of his principal teacher of which Bacon*s Perspediva is full. 
ViteIIo*s tables of refraction have excited much admiration. Tliey prove, how- 
ever, on careful examination to be an almost exact repetition of those of Ptolcmy. 
Whether Bacon and Vitello ever came into contact therc is no evidence 
to show. Bacon was always ready to mention the sources of his knowledge. 
Not so Vitello. If he borrowed from Bacon, he wonld not have said so. 

' It must be owned that where Bacon differed from Alhazen, the advantage 
was not always on his side. Alhazen contended vigor&usly against the view of 
the older oculists that vision took place by visual force issuing from the eye, 
maintaining that the ray proceeded to the eye from the object. Bacon (vol. ii. 
PP- 49 53 "i makes a fruitless attempt to conciliate these opposite views. 



OPTICS. Ixxiii 

convergeace of rays. For such convergence the curvature 
must be other than spherical, it must be that produced by the 
rotation of a conic section. 

Bacon, moreover, is distinguished from the Arabian optical 
writers, and from other investigators of his own time, by his 
sedulous endeavours to tum the discovery of the laws of re- 
flexion and refraction to practical account. Neither in Alhazen 
nor in Vitello is there any attempt to construct instruments 
for the purpose of increasing the power of vision. With Bacon 
this object was always held steadily in view. Of the simple 
microscope he had a perfectly clear conception. His scientific 
imagination played freely with the possibilities of bringing 
distant objects near, and of indefinitely magnifying minute 
objects, by giving suitable directions to refracted rays, and by 
the use of appropriate media. It would be, however, an entire 
exaggeration of his achievements to speak of him as the 
inventor of the telescope. No evidence is forthcoming for his 
having efTected the simple combination of two convex lenses, 
or of a convex with a concave lens, on which the power of 
telescopic vision depends. All that can be claimed for him 
is that he was the first deiinitely and explicitly to bring the 
problem forward, leaving it for after generations to solve. In 
truth, his conception of an optical image, as constructed by the 
assemblage of foci of rays proceeding from each point of the 
object magnified, though in the main correct, was not always 
clearly grasped. Of the distinction between virtual and real 
images, his notion was entirely in default. 

Nor, again, had Bacon a clear conception of the conditions of 
distinct vision. He examined to much better purpose than 
Alhazen had done the structures of the eye ; and he was aware 
of the refraction produced by the curved "surface of the comea, 
and by the doubly convex crystalline lens. But what he 
failed to grasp ' was the necessity of a clear image of the object 
defined on the retina; that image being produced by the 
focussing on the retina of rays proceeding from each point of 
the object. The phenomena of accommodation, produced by 
the action of the ciliary niuscle, which, by altering the curva- 

* Scc vol. ii- p. 159. 



Ixxiv INTRODUCTION. 

ture of the lens, enables rays from near objects to be accurately 
focussed, were unknown to him. But this is only to say that 
he had not anticipated the physiologicai knowledge of the 
nineteenth century. 

It must always be bome in mind that, in Bacon's view, the 
radiation of light through space did not stand aione. It was 
a type of other radiant activities, such as colour (then supposed 
to be distinct from, though dependent on, light), heat, sound, 
and odour. (With regard to sound, however, certain reserves 
were made.) It is interesting to note Bacon's handling of an 
important probiem, not to be solved but by a more potent 
calculus than any in his possession, how these various actions, 
crossing one another's paths in their passage through space, 
retained their distinctness ^. 

IX. Bacon's Alchemy. 

It will be remembered that among the various branches of 
knowledge regarded by Bacon as falling under the head 
of Physics, was Barology {Scientia ponderum), The treatise 
of Jordanus Nemorarius, De Ponderibus, to which reference is 
made, vol. i. p. 169, had perhaps suggested the treatment of 
the phenomena of gravity as a distinct branch of science. 
No treatise by Bacon upon this subject, so far as I am aware, 
is extant ; and the few remarks in the fourth section of the 
Opus Majus (pp. 167-174) contain all that we know of his 
speculations on the theory of gravitation. 

Nor is anything known to us of the way in which Bacon 
treated, if indeed he ever attempted, the science which he 
called * Agricultura/ which, as we have seen, was intended to 
include the study of iiving bodies, vegetable and animai. 
But the case is otherwise with the science regarded by him 
as preparatory to the study of life, • Alkimia Speculativa.' On 
the subject of Alchemy, very little is said in the Opus Majus ; 
and the omission was supplied in the provisional way, which 
alone was possible under the hurry of compilation to satisfy 
Pope Clement's orders, by the Opus Minus^ the first of the 

^ See note on vol. ii. p. 46. 



ALCHEMY. Ixxv 

two appendages to that work. Unfortunately the only text 
of the Opus Minus which we possess has come down to us, not 
merely incomplete, but in so corrupt a state as to render it 
often very difficult to decipher Bacon's meaning. Enough 
remains, however, to show the large and comprehensive spirit 
in which Bacon regarded the subject. 

The contempt expressed in much modern writing for 
mediaeval alchemy might be well retorted on its authors. 
Admit that some prosecutors of the occult art were deceivers 
as well as deceived, and that others were impelled by wild 
hopes of gain, has the pursuit of physical science in modern 
times been whoUy free from similar taints? Electricity 
applied to medicine has been a fertile field for impostors. 
And will any one maintain that the pursuit of chemistry has 
not been stimulated by hopes of industrial profit ? Yet such 
things are not allowed to cast a shade on the names of 
a Lavoisier, a Dalton, or a Faraday. Alchemy was chemistry 
in its prescientific period. Under the guidance of hypotheses 
which were not nearly so wild or crude as they at first appear, 
it attacked, like the true science which gradually grew from 
it, the important problem of the transmutation of matter by 
artificial agencies. It took for granted that metals were 
compound bodies, the elements of which might be separated 
and recomposed. This was no unreasonable supposition. 
Indeed, until modem spectrology had shown that the vapour of 
many metals existed undecomposed in the intense heat of the 
sun's atmosphere, there was no adequate reason for abandon- 
ing the attempt to decompose them. It would be hard to 
find in alchemy any conjecture more baseless than that of 
Phlogiston, the subtle spirit of flame, the loss of which by 
combustion made the oxide heavier than the metal. Yet 
Priestley accepted this hypothesis, and a Lavoisier was needed 
to destroy it 

Alkimia, as conceived by Bacon, fell into two great divi- 
sions — speculative and operative. Under the latter was 
included the metallurgy of the gold-seekers, and generally 
all the practical and industrial processes pursued, with more 
or less wisdom, by men who had a definite purpose in view — 



Ixxvi INTRODUCTION. 

the transmutation of metals, the discovery of the phiiosoph"er's 
egg, or the elixir vitae. But Bacon was one of the few who 
saw that the empirical proceedings of the honest mystics or 
scheming charlatans, who were toiling at their royal road to 
wealth or longevity, covered speculations of a far deeper kind ; 
the study of the transition of matter from the four Aristo- ' 

telian elements, through increasing deg^ees of complexity, up i 

to the highly compound forms exhibited by organized bodies. 
The * Alkimia Speculativa * of Bacon was, indeed, not alchemy 
at all as commonly understood: it was nothing less than 
chemistry. 'Alkimia Speculativa,' he says, in the twelfth 
chapter of the Opus Tertium, *treats of the generation of things 
from their elements, and of all inanimate things — as of the 
elements and iiquids (humores) simple and compound ; common 
stones, gems, and marbles ; gold, and other metals ; sulphur, 
salts, pigments, lapis lazuli, minium, and other colours ; oils, 
bitumen, and very many other things — of which we find nothing 
in the books of Aristotle; nor are the natural phiiosophers or 
any of the Latins acquainted with these things. And being 
ignorant of them, they can know nothing of what foUows in 
physics, that is, of the generation of animate things— as 
vegetables, animals, and man — because knowing not what is 
prior, they must remain ignorant of what is posterior. For 
the generation of men, and of brutes, and of plants, is from 
elementai and liquid substances, and is of like manner with the 
generation of inanimate things. Wherefore, through ignorance 
of this science, neither can natural philosophy, commonly so- 
cailed, be known, nor the theory, and therefore neither the 
practice, of medicine ; not merely because natural philosophy , 

and theoretical medicine are necessary for the practice, but j 

because all simple medicines are derived from inanimate i 

things by this science.' 

Of such fundamental truths of chemical science — as the 
composition of air and water, the theory of combustion, and 
the chemistry of carbon — he, like his contemporaries, was , 

ignorant ; but the ignorance was shared by the second Bacon 
with the first, and was not to be dissipated for five centuries. 
All that could be done in the meanwhile was to collect empi- 



ALCHEMY. Ixxvii 

rical information as to a few metals and their oxides, some of 
the principal alkalis, acids, and salts. On all these things the 
Arab investigators, from Geber downwards, had accumulated 
a considerable mass of material. It is not easy to deiine 
the results of each inquirer, owing to the prevalent habit of 
describing their procedure and results in mystical language. 
Self-defence against charges of magic and imposture was 
probably their motive. And that the danger was real, the 
history of Bacon's life suffices to show. His eflForts to refute 
the charge of magic were incessant. In his treatise, De Secretis 
Operibus Artis ei Naturae ei de nullitate Magiae, he describes 
in detail the various procedures of the magician, sleight of 
hand, ventriloquism, pretended movements of inanimate 
things in dim light, the aid of accomplices, utterance of mys- 
terious formulae, invocation of spirits. We gather from the 
description that the lapse of six centuries has done little to 
change the character of charlatanism. But Bacon was aware 
that the charlatan was often in possession oF valuable secrets. 
' Many books are held to be magical,' he says, * which are not 
really so, but which contain important truths ; which are of 
this kind, and which are not, it is for the experience of the 
wise man to decide. If he find in them any result of natural 
or artificial forces (opus naturae vel artis), let him accept this ; 
otherwise let him reject them as worthless.' Bacon carefully 
guards himself against denial of the mystical force of words 
uttered under solemn conditions, as in the daily miracle of 
the Eucharist, or in the solemn invocations that protected 
the innocent when exposcd to judicial drdeal. Such powers 
might be exerted for good as for evil ; and the unlawful use 
of them was strictly and severely to be condemned. 

But to whatever extent Bacon may have shared the illusions 
of his time with regard to the practical operations of alchemy, 
it is a striking proof of his scientific discernment that under 
the head of Speculative Alchemy he should have formed a 
clear, though distant survey, of chemical science as the inter- 
mediate link between Aristotelian Physics and the science 
of living bodies. As Physics followed on Mathematics so did 
Chemistry, in Bacon's arrangement of the sciences, succeed 



Ixxviii INTRODUCTION. 

Physics. After chemistry came the study of living bodies, 
on which Bacon, while assigning to this science its natural 
place in the series, has said little or nothing. But on the 
study of plants and animals was based, under the name of 
Medicina, the study of the physical structure and functions 
of man. Here Bacon had for his guides, not Galen indced, 
to whom his references are few, but Avicenna, Haly, aad 
a host of Arabian professors of medical art, to whom Galen 
had supplied a very substantial foundation of anatomical and 
physiological knowledge. Bacon*s short treatise, to which 
reference is occasionaliy made in the Opus Majus, De re- 
tardaiidis senectutis accidentibus^ wili sufficiently illustrate 
his views on this branch of science. 



X. EXPERIMENTAL SCIENCE. 

Last among the series of the natural sciences comes that 
which Bacon denotes as 'Scientia Experimentalis.' The 
sample of it, for it can hardly be regarded as more than 
a sample, given in the sixth section of the Opus Majus 
indicates that it was connected in Bacon's mind with no special 
department of research, but was a general method used for 
the double purpose of controlling resillts already reached by 
mathematical procedure, and of stimulating new researches in 
fields not as yet opened to inquiry. 

In some respects this is the most original part of his work. 
Not that experiment was a new thing. Experiments without 
number had been made by man from the time of his first 
appearance on the planet. The Greeks towards the end of 
their marvellous scientific career had b^un to use experiment 
in their investigations of natural truth. Galen had applied it 
in his researches into the nervous system ; Ptoiemy had arrived 
by its means at his remarkable discovery of the refraction of 
light. The Arab astronomers, far more skilfui mechanicians 
than the Greeks,had constructed extremely elaborate apparatus 
for the same purpose, and also to verify the equality of the 
angles of incidence and reflection. But no one before Bacon 
had abstracted the method of experiment from the concrete 



EXPERIMENTAL METHOD, Ixxix 

problem, and had seen its bearing and importance as a uni- 
versal metliod of rcsearch. Implicitly men of science had 
begun to recognize the value of experiment What Bacon 
did was to make the recognition explicit. . Experiment took 
its place as a distinct department of philosophy. 

What makes this result peculiarly remarkable is that it was 
reached by a thinker who was so profoundly penetrated by 
the mathematical spirit. In this matter Roger Bacon compares 
favourably with his illustrious namesake of the seventeenth 
. century, who wholly failed to appreciate the import of mathe- 
matical method. He rises to the level of one greater than 
either — the author of the Discours sur la MHkode. For 
Descartes as for Roger Bacon, mathematics was clavis 
scientiarum, the key to the temple of science. But it was 
held by both alike that experiment was needed to carry out 
the researches which mathematical deduction had suggested ; 
and that, as each science grew, the share taken by experiment 
in its progress was to become more and more predominant 

XI. MORAL Philosophy. 

Last in order, both in the Opus Majus and in the Scriptum 
Principale^ comes the science the study of which is the key- 
stone and crown of the whole work — the science of life and 
conduct AII the other sciences lead up to this. Their con- 
clusions form its point of departure. 

The analysis which has been given of this, as of other parts 
of the work, renders it unnccessary to cover the ground a 
second time. But a few remarks may be made on its salient 
features. In the first book, which treats of man's relation to God, 
Bacon follows the procedure common to Aquinas, indeed to most 
of the schoolmen, of pushing metaphysical reasoning as far as 
it can be made to go in support of the articles of the Catholic 
faith. Theolc^y, says Aquinas (5. T. Pars I. Quaest. i. art. 5), 
uses other sciences as her handmaids and assistants. Man is 
more easily led on to things above reason, if he begins with 
things which reason can demonstrate. It is true that unassisted 
reason is incompetent to discover and demonstrate the doctrine 



Ixxx INTRODUCTION, 

of the Trinity. * Impossibile est/ he says (Quaest. xxxii. 
art. i), 'per rationem naturalem ad cognitionem Trinitatis 
divinarum personarum pervenire.' But he goes on to explain 
that there are two modes of employing reason. One is to 
discover and prove a principle : as in physics we prove the 
uniformity of the motion of the heavens. The second mode 
is, when the principle is admitted, to show that certain observed 
effects are consistent with and follow from it. So, for instance, 
assuming the reality of our hypotheses as to eccentrics and 
epicydes, we can show that the movements of the planets 
take place in accordance with these hypotheses. It is this 
latter form of reasoning that we use in reference to the 
Trinity. * Trinitate posita, congruunt hujusmodi rationes.* 
We find analogies with this doctrine when we consider what 
passes in our own minds. ' Ipse conceptus cordis de ratione 
sua habet quod ab alio procedat, scilicet a notitia concipientis * 
(Quaest. xxxiv. art. i). 'Quanto aliquid magis intelligitur, 
tanto conceptio intellectualis est magis intima intelligenti et 
magis unum . . . unde cum divinum intelligere sit in fine per- 
fectionis . . . necesse est quod Verbum divinum sit perfecte 
unum cum eo a quo procedit, absque omni diversitate ' (Quaest. 
xxvii. art. i). Similarly (art. 3), the procession of the Third 
Person is likened to the operation of the will Which we call in 
human beings love. *Processio Verbi attenditur secundum 
actionem intelligibilem. Secundum autem operationem volun- 
tatis invenitur in nobis quaedam alia processio, scih'cet processio 
amoris, secundum quam amatum est in amante, sicut per 
conceptionem verbi res dicta vel intellecta est in intelligente. 
Unde et, praeter processionem Verbi, ponitur alia processio in 
divinis, quae est processio amoris ^' 

Bacon, as we might expect, was not less eager to find the 
mysteries of revelation foreshadowed by human reason. 
Holding, as he has fully explained in the second part of the 

* It is perhaps hardly necessary to refer in this connexion to Hampden s 
lectures on Tki Scholastic Philosophy considered in its relation to Christian 
Theology, Compare p. 8i (second edition), * The object of the Scholastic 
Tbeology was to detect and draw forth from the Scripture, by aid of the sjibtle 
analysis of the philosophy of Aristotle, the mystical truths of God on which 
the Scripture Revelation was conceived to be founded.' 



MORAL PHILOSOPHY. Ixxxi 

Opus MajuSy that the rise and progress of Greek philosophy 
was no less a part of divine providence than the succession of 
the priests and prophets of Judaea, he found without surprise 
that Aristotle, Plato, Porphyry and others had apprehended, 
more or less dimly, some of the fundamental tniths of Christian 
theology ; among them being the Trinity, the Incamation, the 
existence of angels and the resurrection of the body. Moral 
philosophy, as Bacon conceived it, was in every respect con-^ 
current with theology. ' De iisdem negotiatur quibus theologia, 
licet alio modo.' It is perhaps more surprising that he should 
have gathered these truths not merely from Greek and pre- 
Christian writers, but from the great Mahommedan teachersi 
such as Albumazar, Avicenna, and Algazel. Some of the 
most remarkable passages in the first part of his moral 
philosophy are quotations from Avicenna. More than once 
he refers to tbe passage in which Avicenna, speaking of future 
life in thc unseen world, observes: Our present relation to 
that life is like that of the deaf man who never listened to the 
delights of harmony, though he never doubted that such 
delights existed. Or again : We are like the palsied man to 
whom delicious food is offered which yet we cannot taste till 
the palsy be healed. Avicenna tells us how the soul's vision 
is clogged by bodily impulses, and limited by the obtruding 
influences of the visible world ; and he insists on the need of 
purging the soul from sin, of concentration of its forces on 
invisible things, and of acceptance of revealed truth. We 
may well believe that the attempt to level up Mahommedan 
philosophers to the level of Christian teachers was among the 
fwvitates for which Jerome d*Ascoli cut short Bacon s philo- 
sophical career. 

The second part of the Moral Philosophy, dealing with the 
laws of civil and sociai life, is summarily disposed of in two 
short chapters. Possibly a reason for this cursory treatment 
may be found in Bacon's aversion to the introduction of 
Roman law, which finds vehement expression in the twenty- 
fourth chapter of the Opus Tertium, and again in the Cotft'' 
petidium Studii (Brcwcr, pp. 84-87, and 418) ^. 

' Something additional on this subjcct was probably said in the missing sixth 
VOL. I. f 



Ixxxii INTRODUCTION. 

We are here brought face to face with thc fallure, and the 
cause of the failure, of Bacon s social and political ideal. He 
was aiming at an enlarged and renovated Catholicism which 
shouid bind together and incorporate all that was best and 
noblest in Hebrew, Greek, and Arabic tradition in the fabric 
of the Christian Church, for the spiritual government of the 
world. The keystonc of the fabric was supplied by the 
mistress-scicncc, theology, resting on Mosaic and Christian 
revelation, consolidated by Aristoteh'an philosophy, and 
penetrated by thc vital and progressive spirit of natural 
sciencc. A progressive papacy, carrying on in continuous 
and harmonious devclopment the work which Mosaic law and 
Greek intellect had b^un — ^such was Bacon's vision : and the 
marvellous upheaval of thought in Paris and elsewhere during 
the thirteenth century seemed to bring that vbion within reach 
of fulfilment. 

But while Paris was building up its systems of philosophic 
theology, south of the Alps, in the rival university of Bologna, 
work of another kind was going on. The study of thc civil law 
of Rome, which had never wholly ceased in the cities of North 
Italy, had been stimulated early in the twelfth century by the 
teaching of Irnerius and others ; and from that teaching the 
university of Bologna gradually arose, as the university of 
Paris had arisen from the teaching of Abelard. It was 
a momentous event in the history of Europe. Civil law was 
a study as secular as the Roman empire itself. Clerical and 
lay students sat at the lecturcs side by side. * Very carly in 
the twelfth century mcn of mature age, men of good birth and 
good position, beneficed and dignified ecclcsiastics, or sons of 
nobles, flocked from the remotest parts of Europe to the 
lecture-rooms of Bologna ' (Rashdall, Hisiary of Universities^ 
i. 124). The civil law embraced the entire system of man's 
social relations, and dealt with them on principles with which 
thcology had no conccrn. 
. The Church felt the danger, and coped with it in the only 

part of the Moralis Philosophia. But his language on the subject does not 
warrant the belief that the subject was fully dealt with. Cf. Op, Ttrt, cap. xiv. 
Brewer, p. 59. 



MORAL PHILOSOPHY. Ixxxiii 

way that was possible, by borrowing weapons from her lay 
rival, and arranging her own system of law in a form not 
less comprehensive and systematic. Irnerius had hardly 
jinished his lectures when a fellow-citizen, the monk Gratian, 
in 1143 published his great text-book of canon law known 
as the Decretum^ to which, in 1 234, Gregory IX added five 
books of Decretals. 

Nominally the situation was saved, but at the cost of 
secularizing the Church. For the canon Uiw was in reality 
based on the civil law. * Everything in the canon law was 
Roman which was not of directly Christian or Jewish origin.' 
' After the age of Gratian the studies even of ecclesiastics 
took a predominantly legal tum. Speculative theology was 
abandoned in favour of the canon and even of the civil law ; 
while the estrangement of thc canon law from theolc^ 
kept pace with the increasing closeness of its union with 
the faculty t>f civil law' (Rashdall, i. p. 138). In 12 19 
Honorius III formally prohibited the study of civil law in 
Paris on the ground that it threatened to extinguish the study 
of theology in the one great theological school of Europe. 
But prohibitions that were powerless to exclude Aristotle 
were equally impotent against the invasion of Ulpian and 
Justinian. 

Bacon's pages reflect very vividly the conflict of clerical 
with secular influences. ^ More praise,' he says, ' is gained in 
the Church of God by a civil jurist, though he may know 
nothing but civil law and be utterly ignorant of canon law 
and theology, than by any master in theology, and he is more 
quickly promoted to high ecciesiastical positions/ ' Oh that 
the canon law might be purged from the superfluities of civil 
law, and be ordered by theol<^/ he exclaims, ' then would 
the govemment of the Church be carried on honourably and 
suitably to its high position' {Opus Tertium, ch. 24). 

He recurs to the same subject in a later work. 'For the last 
forty years the abuse of the civil law of Italy has been under- 
mining not merely the study of philosophy, but the Church of 
God, and all the kingdoms of Christendom.' ' They monopo- 
lize/ he proceeds to say, ' every office of emolument, 80 that 

1% 



Ixxxiv INTRODUCTION. 

students of theology and philosophy are deprived of the 
means of foUowing their studies. And besides this, the study 
of civil law is obliterating the distinction between clerical and 
lay professions. The doctors of law of Bologna call them- 
selves clerks and masters, though they have not the tonsure, 
though they take to theniselves wives, have families, and in 
every respect adopt the ways and practices of laymen . . . If 
clergymen and laymen arc to be subject to the same law, at 
least let it be the law of England for Englishmen, and of 
France for Frenchmen, and not the law of Lombardy ' {Com* 
pendium Studiiy cap. 4) ^. 

When Bacon appealed to the Pope to arrest the diffusion 
of civil law, he was like one who should attempt to stop the 
tide or the courses of the stars. He was fighting against the 
laws of historical evolution. It was written that the constitu- 
tion of society should be settled on a human and secular, not 
on a theological basis ; and the study of civil law, radiating in 
the twelfth and thirteenth centuries from Bologna into every 
part of Christendom, was one of the most significant among 
noany signs that the function of the Catholic Church, as the 
oi^anizer of political society, was gone. 

Widely different was the future of that Church in all that re- 
lated to personal morality. Yet here too there was much to be 
desired. In the third section of thc work this subject is discussed 
with grcat fullness. 'On virtue and vicc,' says Bacon, 'thc 
ancient philosophers have spoken so wonderfuUy that a Chris- 
tian man may well be astounded at men who were unbelievers 
thus attaining the summits of morality.' ' On the Christian 
virtues of faith, hope, and charity,' he adds, 'we can speak 
things of which they knew nothing. But in the virtues necded 
for integrity of life, and for human fellowship, we are not their 
equals either in word or deed. Blameworthy and shameful in 
us that it should be so.' Acting on this view, Bacon has 
composed this third part almost entirely of selections from 

* This was written (as Brewer shows, p. Iv) in 1271, three years aftcr the 
death of Clement IV. Guy Fulcodi, before his ecclesiastical career began. had 
been a distinguished lawyer, and would hardly have tolerated such strong 
language. 



MORAL PHILOSOPHY. Ixxxv 

Aristotle, Plato, Cicero, and above all, from Seneca, adding 
the fewest words of his own that were needed to mould them 
into systematic shape. 

He begins by adopting Aristotle'8 general scheme of the 
moral virtues as means between opposing vices. From these 
he passes to the consideration of special vices in the order 
of the seven mortal sins of Catholic theology. ' Six of these 
deal with man's conduct under prosperous circumstances ; 
the seventh, anger, with his conduct in adversity. Dealing 
briefly with the first class, Bacon devotes much more atten- 
tion to the subject of anger. His reason for doing so lay in 
the disturbing influences of this passion on the whole of man s 
life public and private, and also that, in seeking remedies for 
its ravages, we are led up to the state of inward peace and 
resignation under outward trials which forms the highest plane 
to which the soul can aspire. 

Nearly the whole of Seneca's three dialogues on Anger are 
quoted, but with complete rearrangement, in pursuance of the 
aim in view. Beginning with a picture of this passion and its 
disastrous eflects on the highest qualities of the soul, such as 
clcmency, pity, and joy, he enlarges on examples of self- 
restraint, and thcnce procecds to consider remedial action; 
patient inquiry, time allowed for the mood to pass by, 
and const^nt remembrance of human fellowship- with the 
oficnder. 

This Icads him to the wider subject of fortitude undcr 
calamity, of forgivencss of injury and insult, of rccognition of 
thc truth that whoni God loves Hc chastens. He concludes 
the scction with loi^ selcctions from the dialogues on consola- 
tion under bcreavement, exile, and poverty, on the shortness 
of life and the state of inward bliss and spiritual peace. It 
appears that though other parts of Seneca wcrc well known, 
espccially the scries of lcttcrs to Lucilius, these dialogucs had 
cscapcd notice till Bacon callcd attention to them. The 
apocryphal corrcspondencc between Seneca and St. Paul 
shows that an aflinity betwcen Scneca and Christian teaching 
had becn widcly recognized in the Church. Nowhcre is this 
aflinity so strongly marked as in the dialogucs De Providentia^ 



Ixxxvi INTRODUCTION. 

De Vita Beata^ and De Tranquillitate Animi^ from which Bacon 
has quoted so largely. 

The fourth section of the Moral Philosophy contains the 
first attempt ever made at the comparative study of the 
religions of the world. These Bacon ranges in six classes : 
Pagans, Idolaters, Tartars, Saracens, Jews, Christians. What 
specially called attention to this subject in Bacon's time were 
the events proceeding in Central Asia, and already seriously 
affecting European politics. Mongol hordes had swept over 
Russia and South Eastern Europe, and were threatening the 
Western kingdoms. Franciscan and Dominican missionaries 
had been sent by Pope Innocent IV and by Louis IX to 
investigate the danger at its source. The reports brought 
back by these missionaries, especially those of Carpini and 
Rubruquis, brought the reh'gious problem before the view of 
the leaders of the Church in all its magnitude. It was seen 
that beyond the Christian world, beyond the Mahommedan 
world which bounded it, there lay regions of unsuspected 
magnitude in the extreme East, where other creeds prevailed. 
One of these was Buddhism, recently imported into Central 
Asia from Tibet, with its elaborate monastic system, its image- 
worship, and its complicatcd liturgy, This creed was always 
spoken of by Rubruquis and Carpini, as by Marco Polo in 
the succeeding generation, as Idolatry. Christianity of the 
Nestorian type was widely disseminated ; though not, it would 
seem, in its most highly militant form. Side by side with 
these were tribes whose religion was of a lower grade, not 
rising above the rudest fetichism ; these were spoken of as 
Pagans. Between these various modes of faith the Tartar 
chiefs held a doubtful and almost neutral attitude. If these 
could be brought within the pale of the Catholic Church, 
Mahommedanism, crushed between the forces of the West 
and the extreme East, would cease to be a danger. The 
issue remained undecided in Bacon's time. But we can 
imagine with what interest he would confer, ,as he tells us 
that he did, with Rubruquis on his return to Paris, and 
listen to his story of the Parliament of Religions, Saracen, 
Christian^ and Buddhist, held at Kara Korum at the sug- 



MORAL PHILOSOPHY. Ixxxvii 

gestion, and under the presidence^ of Mangu Kaan. (Cf. 
vol. ii. p. 389.) 

In Bacon's demonstration of the superiority of Christianity 
to other religions, use is made of this singular experiment. 
The majority of those who took part in it accepted the unity 
of God. The Pagans were few in number. The Buddhists 
(spoken of as Idolaters) raised the question of the origin of 
evil as an objection to a single ruler of the Universe ; but 
they allowed the question to be evaded. The Tartars, though 
somewhat indifferent on religious matters, were' disposed to 
side with the Mahommedans and Christians in maintaining 
the unity of God. On the whole, the conclusion to which 
this conference tended was a fair sample, in Bacon*s judgement, 
of the preponderating voice of mankind. 

Appeal is then made to Aristotelian reasoning as to the 
necessity of a First Cause. The attributes of wisdom and 
goodness are shown to follow from omnipotence. Man's duty 
being to do God's will, how is man to know it? Evidently 
by revelation. And which revelation is true ? There can be 
but one : for if there were more the human race could not 
be united. * The unity of the Church follows from the unity 
of God. If there were more Gods than one, more worlds 
than one, and more mankinds than one, then there might be 
more revelations than one, but not otherwise.' Which, then, 
is the true revelation ? On a comparison of the six religions 
before us, three, the Pagan, the Buddhist, and the Tartar, are 
at once ruled out. Of the three that remain, the Jewish, the 
Saracen, and the Christian, philosophic reasonii^, extemal 
and miraculous evidence, and ethical purity combine in giving 
preference to the last. The book, as we have it, closes 
with some ardent and rapturous words on the Sacra- 
ment of the Altar, as the means whereby Christ always 
remains present with His Church. 

Of the missing books we are not left in entire ignorance. 
We know from the fourteenth chapter of the Optis Terttum 
that the purpose of the fifth book was, to insist upon such 
modes of setting forth moral truth as were likely to impress, 
not merely the intellect, but the emotions and character of 



fxxxviJi INTRODUCTION. 

the hearer. The art of preaching, Bacon thought, was one 
demanding the most serious and systematic study. Rhetoric 
was no mere field for the gratification of vanity by omamental 
display. It was a part of logic, and the most important part, 
since by its means truth was so conveyed to the li.stener that 
* he is seized unawares and lifted above himsclf and filled with 
thoughts beyond his power to control, so that if evil he is 
absorbed by the love of good, if imperfect he receives the 
spirit of perfection, not through violence, but through the 
strong and gentle power of speech.' Rhetoric thus conceived 
implied the study of music in its widest sense, the study of 
rhythm and metre, the management of voice and of gesture 
{Opits Tertium, ch. 75). 

The sixth and final section of Bacon^s moral philosophy 
treated, he says, of lawsuits and of justice. He implies, how- 
ever, that he dealt with this subject cursorily. 

XII. General Characteristics of the Opus Majus. 

The question presents itself, How far can the Opus MajuSy 
with its two appendices, the Opus Minus and the Opus Ter- 
iium^ be accepted as the final exposition of Bacon's philosophy 
and polity? It is spoken of by the author throughout as a 
persuasio praeambula. It is a hortatory discourse addressed 
to a busy statesman ^for Clement IV, like most other popes 
of the thirteenth cenlury, may be so called), urging him to 
initiate a reform of Christian education, with the direct object 
of cstablishing the ascendency of the Catholic Church over 
all nations and rellgions of the world. 

A fundamental principle with Bacon was that truth of what* 
ever kind was homogeneous. * AII the sciences,' he said, 'are 
connected ; they lend each other material aid as parts of one 
great whole, each doing its own work, not for itself alone, but 
for the other parts : as the eye guides the whole body, and 
the foot sustains it and leads it from place to place. As with 
an eye tom out, or a foot cut off, so is it with the different 
dcpartments of wisdom ; none can attain its proper rcsult 
scparately, since all are parts of one and the same complete 



THE OPUS MAJUS. Ixxxix 

wisdom ' {Op. Tert ch. 4). Much light is thrown by passages 
like these, and there arc many such, on the varied and at first 
sight heterogeneous character of the Opus Majus. A glance 
at the Index of this edition wlU give some notion of the 
multiplicity of the topics treated. History of philosophy, 
comparative philology, mathematics, astronomy, geog^raphy, 
optics, the physiology of sensation, all find a place ; and all 
are subordinated to the service of the Catholic Church as the 
guardian of the highest interests of man. AIJ these topics 
are handled so far and in such a way as to convince the Pope, 
or othcrs in authority, of the width of the field to be culti- 
vated, and of the importance of the object in view. Bacon's 
procedure is like that of a traveller in a new world, who brings 
back specimens of its produce, with the view of persuading the 
authoritics of his country to undertake a more systematic 
expioration. To that further and more complete inquiry he 
proposed to devote the remainder of his life. Hc speaks of 
it in several pas«ages of the present work undcr the title 
of Scriptum Principale. But, as we have reason to believe, 
of the twenty-five years of life that remained, more than half 
werc sterilized by his imprisonment. When released, though 
hc pcrsevered, like Galileo, indomitably to thc end, he was 
too old to think with his former vigour, and was capable only 
of such inferior work as the Compeftdium Theologiae^ or the 
Commentary on the Secreium Secretorum. There remain 
thc years betwecn 1268 and 1278. They produced the Com-- 
pendium Studii (published by Brewer), the Communia Natu- 
ralium^ the Communia Mathematicae, and other fragments 
of the Scriptum Principale, But, making large allowance for 
what may have been lost through neglect or through malig- 
nant hostility, or for what may yct remain to be discovered, 
thc balance of probabilities indicates clearly enough that the 
Scriptum Principale was never brought to completion. Thc 
Opus Majus remains the one work in which the central 
thought of Bacon is dominant from first to last ; thc unity 
of science, and its subordination to the highest ethical pur- 
posc conceivable by man. 

Another characteristic of Bacon*s philosophy, to which it 



xc INTRODUCTION. 

seems to me that sufficient attention has not yet been called, 
is the sense of historical continuity by which it is pervaded. 
Not indeed that Bacon stood alone in this respect. Comte, 
in a remarkable passage of his appreciatton of the mediaeval 
Church, called attention, perhaps for the first time, to the 
awakening of the historic sense which the very constitution 
of that Church involved ; rising as it did from the threefold 
root of Roman law, Greek thought, and Hebrew theocracy 
{Philosophie Positive^ vol. v. p. 247, ed. Littr^). As an example 
of this influence, he proceeds to quote the example of Bossuet, 
one of the first of European thinkers to form, in however 
imperfect a way, a broad and definite conception of the unity 
of history. But the example of Roger Bacon, writing four 
centuries earlier, is even stronger and more startling. Two 
centuries before the Renascence, he states explicitly what 
others may have implicitly thought, but would have shrunk 
from avowing even to themsclves, that the whole course of 
intellectual development of mankind from the beginning of the 
world was not multiple but one, not discrete but continuous. 
He takes pains to synchronize the demi-gods, the heroes and 
the thinkers of Greece with the kings and prophets of Judaea. 
In his conception, philosophy, science, and religious truth had 
a common origin with the patriarchs: though separated in 
later centuries, they pursued a parallel course in Judaea and 
in Greece. The growth of science, no less than the growth 
of religion, was a process of continuous evolution, taking place 
under divine guidance. It may be said that traces of such 
a doctrine as this may be found here and there in the early 
fathers, and especially in the writings of St. Augustine. But 
a comparison of the ninth and tenth books of De Civitate Dei 
with the second and seventh sections of the Opus Majus^ will 
reveal a profound difference in the mode of treatment, even 
more than in the conclusions reached. What the earlier 
writer looks at as concessions wrung from an opponent, the 
later hails as the testimony of a friend. Augustine dwells on 
the points that separate the Christian from Porphyry and 
Seneca ; Bacon on the points of union. 
There are students of history even yet surviving to whom 



THE OPUS MAJUS. xci 

the centuries following the fall of the Western Empire seem 
a chasm hard to pa$s ; so that they prefer, with Vico, to con- 
ceive of an ancient civilization which has run its course, and 
a new cycle as b^inning. For Roger Bacon the apparent 
breach of continuity was in great part filled up by the long 
series of thinkers and students, who kept the torch of science 
alive in the Mahommedan schools of Mesopotamia and Spain. 
A glance at the Index to this edition will show the use which 
Bacon made of such men as Thabit ben Corra, Alfarabius, 
Alfraganus, Alkindi, Alhazen, Albumazar, Avicenna, Hali, 
and Averroes. They are spoken of, and most truly, not 
merely as the principal channels through which Greek philo- 
sophy and science were introduced to the Westem world, but 
as having increased the treasure entrusted to them ; a treasure 
which the Westerns of the thirteenth century, * unless they are 
dolts and asses,' will regard it as their duty to transmit with 
due interest to their posterity. 

At the close of these introductory remarks, some attempt 
may be made to assign Bacon*s position in the history of 
human thought. It appears on the surface that he belongs 
to the order of thinkers, typified by Pythagoras rather than 
by Aristotle, who engage in speculation, not for its own sake 
alone, but for social or ethical results, that are to follow. His 
protests against the intellectual prejudices of his time, his 
forecasts of an age of industry and invention, the prominence 
given to experiment, alike as the test of received opinion and 
the guide to new fields of discovery, render comparison with 
his great namesake of the sixteenth century unavoidable. Yet 
the resemblance is perhaps less striking than the contrast. 
6etween the fiery Franciscan, doubly pledged by science and 
by reh*gion to a life of poverty, impatient of prejudice, 
intolerant of dullness, reckless of personal fame or advance- 
ment, and the wise man of the world richly endowed with 
every literary gift, hampered in his philosophical achieve- 
ments by a throng of dubious ambitions, there is but little in 
common. In wealth of words, in brilliancy of imagination, 
Francis Bacon was immeasurably superior. But Roger Bacon 
had the sounder estimate and the firmer grasp of that com- 



xcii INTRODUCTION. 

bination of deductive with inductive method which marks the 
scientific discoverer. Finally, Francis Bacon was of his time ; 
with Roger Bacon it was far otherwise. 

M. Haur^au, the historian of Scholastic philosophy, and 
also M. Renan, have suggested a parallel (or, it may be, have 
adopted it from Littr^) between Roger Bacon and Auguste 
Comte. Some anticipation of the Philosophie Positive there 
assuredly is in Bacon's subordination of metaphysic to science, 
in his serial arrangement of the sciences, and in his avowal 
of a constructive purpose as the goal of spcculative inquiry. 
But it is well not to push such comparisons too far. We 
shall best understand Bacon*s life and work by regarding him 
as a progressive schoolnian. Like the other great schoolmen 
of the thirteenth century, he set before himself the purpose 
of strengthening the Church in her work of moral regenera- 
tion, by surrounding her with every intellectual resource. 
But the forces that he brought to bear were not limited, like 
theirs, to the stationary dialectic of Aristotle ; they were also, 
in great part, drawn from the prc^ressive culture of natural 
and historical science. As compared with his successors of 
the Renascence, his purpose was loftier; for, in urging the 
continuous advancement of knowledge, he had higher things 
than knowledge in view. His aim, pursued in no spirit of 
utilitarian narrowness, yet steadily concentratcd on the 
moral progress of mankind, was, Induire pour dMuire afin de 
construire. 



ANALYSIS OF THE 'OPUS MAJUS/ 
PART I. 

THE FOUR GENERAL CAUSES OF HUMAN IGNORANCE. 

CHAPTER I. 

VOL. I. PAGES 

True wisdom implies— i. Sound methods of gaining knowlcdge; 
2. The application of knowledge to important purposes; as the 
govemment of the Church, the conversion of the heathen, and 
the repression of evil-doers. Such wisdom is hard to obtain, and 
there are four principal causes of failure. These are — i. Subjection 
to unworthy authority. 2. The influence of habit. 3. Popular 
prejudice. 4. False conceit of our own wisdom. We will begin by 
dealing with the three first : the fourth demands separate tieat- 
ment 1-4 

CHAPTER 11. 
Opinionsoif philosophers on these defects,— Citations from Aristotle, 
Seneca, Cicero, Averrhoes, Abelard, Jerome, Chrysostom . . 4 6 

CHAPTER III. 
Leaving authority, let us look to experience. Authority, habit, 
and prejudice may sometimes lead to truth, but the probabilities 
are much against it. We may take an illustration from arithmetic. 
Of perfect numbers, there is but one among the first ten, one 
between 10 and 100, one between 100 and 1,000, one between 1,000 
and 10,000. Among men the number of the truly wise is even 
smaller. Even of philosophers few are to be counted among them. 
Aristotle, the wisest of all, was not perfect 6-8 

CHAPTER IV. 
Of the three first causes of error, popular prejudice is the most 
potent The truth that pearls should not be cast before swine is 
confinned by Aristotle and other philosophers .... 9-11 



xciv ANALYSIS OF THE ' OPUS MAJUS/ 

CHAPTER V. 

VOL. I. PAGES 

Continuation of the subject. Gratitude is to be shown to the 
great founders of truth even where they have fiailed . • .11-13 

CHAPTER VI. 
Errors are infinite, truth single. New generations inheriting the 
results of their predecessors can see their mistakes. Avicenna sees 
where Aristotle erred; Averroes corrects Avicenna. Among the 
fathers of the Church we see the same thing. They acknowledge 
their own errors and point out those of others • . . • 13-15 

CHAPTER VII. 
Further illustrations, justifying cautious scrutiny of received 
opinions 15-17 

CHAPTER VIII. 
By habit of discussing received opinion we cease to be s!aves 
toit 17 

CHAPTER IX. 
But the fourth source of error, false conceit of our own wisdom, is 
far the most dangerous. It fortifies itself with the results of the other 
three by endowing this false wisdom with the force of authority, of 
custom, and of popular prejudice. Prior to the detection of the 
symptoms of this spiritual disease, we must acquire, as physicians of 
the body do, some knowledge of universal causes from the study 
of nature (communia naturalium). The potency of this source of 
error is shown by historical examples 17-21 

CHAPTER X. 
Two things are to be distinguished : presumption of knowledge ; 
concealment of ignorance. What each one of us can know is little 
in comparison with what faith reveals; but both together are as 
nothing to the unknown world which neither ^th nor reason can 
reach. Why then boast of knowledge ? The labours of a long life 
can be assimilated by an intelligent boy in a year. If this boy has 
leamt at the right source he will be further advanced than many of 
his leamed seniors, as the youth entrusted with this work will prove. 
Wise men know their ignorance, and are ready to leam from every 
one. I have learaed more from plain men quite unknown to fame 
than from all the doctors 21-23 

CHAPTER XI. 
The evil tends to multiply itself owing to the claims set up by 
ignorance to authority. Yet men^ however leamed they may be in 



PART I. xcv 

VOL. I. PAGES 

other ways, should be credited with no authority whatever in things 
of which they know nothing 23*24 

CHAPTER XII. 
Many things known to the ancients we neglect, as the study of 
mathematics and languages, from sheer ignorance of their value. In 
other cases the fact that subjects are not studied by the fathers is 
held a good reason for passing them by. We forget that the saints 
and fathers were justified by the circumstances of their time, and 
moreover that they were not infallible. Augustine found much fault 
with Jerome, and so in other cases 24-26 

CHAPTER XIII. 
We must remember that the best Greek work was not known to 
the Latin fathers. Plato indeed was translated and carefuUy studied ; 
but Aristotle, from the very fact of being Plato's opponent, was 
neglected. Yet Augustine had translated the Categories, a work 
highly valued by Alcuin. Boethius also translated some of the 
logical works. But if the greater works of Aristotle had been known 
to them, they would have gladly received these, and not have troubled 
themselves about the asbes of his philosophy .... 26-28 

CHAPTER XIV. 
The early Church made no use of Greek science except for the 
purpose of regulating its calendar and its music. The explanation 
of this neglect of ancient leaming is fivefold. i. PhOosophy was the 
foundation of law and govemment to all the nations of antiquity 
except the Hebrews. 2. Therefore it was that philosophy resisted 
Christianity. 3. Moreover these nations not merely studied philo- 
sophy, but practised auguryand oracular magic. 4. Theypersecuted 
Christians. 5 The Church, finding her enemies occupied on the one 
hand with the study of philosophy, and on the other with the study 
of magic, associated these two things, and thus came to despise and 
dislike philosophy. The tmth is however that phiiosophy, so far from 
being hostile to the Church, is capable of yielding it indispensable 
support 28-30 

CHAPTER XV. 
Later ecdesiastical authorities have followed a similar course, 
though without the excuse which justifies the early iathers. Though 
Greek philosophy is no longer untranslated, they study only its most 
trivial productions, neglecting the great works of science and 
ethic 30-31 



xcvi ANALYSIS OF THE ' OPUS MAJUS/ 

CHAPTER XVI. 

VOL 1. PAGES 

Let me not be misunderstood. I am not proposing to your HoH- 
ness any violent change in the ordinary course of studies. I am 
merely suggesting free access to a land of plenty for those who care 
to avail themselves of it. If once the leaders of thought become more 
enlightened, the rest will soon follow 31-32 



PART II. 

THE CONNEXION OF PHILOSOPHY WITH THEOLOGY. 

CHAPTER L 
Theology is the mistress-science. All truth is contained in the 
Scriptures ; but to elicit truth we need the help of the canon law 
and of philosophy. Wisdom comes from one God, is given to one 
world, for one purpose. Itself therefore is one. It cannot be 
inconsistent with itself 33-34 

CHAPTER IL 
The canon law has its root in Scripture. From that root spring 
branch and fruit ; the teaching of the fathers and doctors of the 
Church and the rules finally laid down by them .... 34-35 

CHAPTER IIL 
So with philosophy. Augustine dwells at length on the importance 
of taking from it all that is precious, as the Hebrews of old borrowed 
jewels from the Egyptians. He included in the word ethics, history, 
knowledge of the arts, logic, and grammar 35-37 

CHAPTER IV. 
Jerome and Bede used similar language. Bede remarks that, as 
Solomon when buiiding his temple called foreign workmen to his aid, 
so has Christ availed himself of heathen philosophers in building his 
Church. Paul, too, quotes heathen poets 37-38 

CHAPTER V. 

Wherever truth is found it belongs to Christ. We must distinguish 

between inteUectus agens and intellectus possibilis, The first is no 

part of our nature. Our minds are capable of receiving it and of 

being stirred to action by it, but it comes from without. This can be 



PART II. xcvii 

VOL. I. PAGES 

proved from Aristotle, when rightly interpreted, and from his com- 
mentators Alpharabius and Avicenna. Reason comes from God: 
therefore philosophy is divine 38-41 

CHAPTER VI. 

But we may go farther. Wisdom was a direct revelation of God to 
the philosophers of antiquity. Aristotle, Cicero, and Augustine may 
be cited to show this 41-42 

CHAPTER VII. 

Indeed the very purpose of philosophy is to lead up through know- 
ledge of the creature to knowiedge and service of the Creator . 42-43 

CHAPTER VIII. 

The Scriptures tell of the creature, and reveal its final cause : 
leaving the efficient cause to be dealt with by philosophy, which as 
yet has but imperfectly done her work. The rainbow is an illustra- 
tion 43-44 

CHAPTER IX. 

The most important point of all has now to be explained. Philo- 
sophy is not an invention of heathen nations : it was revealed in its 
entirety to the first patriarchs, by the same Spirit who revealed to 
them the oracles of God. We leam from Josephus that Noah and 
his sons taught the Chaldaeans; Abraham the Egyptians. That 
philosophy originated with the patriarchs is admitted by Aristotie. 
From the Chaldaeans and Egyptians, thus taught, further progress 
ensued, the history of which may now be traced in parallel lines with 
that of the Hebrews. Isis and Pallas were contemporary with Jacob 
and Esau. Under Phoroneus, the second king of the Argives, a few 
years later, moral philosophy was first taught. Then came Prometheus 
and Atlas, contemporary with Moses. Hermes was the grandson of 
Atlas ; by him or by another wise man, ApoHo, Asciepius was taught, 
the founder of medical art ; though probably medicine was better 
known to the sons- of Adam and Noah, who thus atlained great 
longevity 44-49 

CHAPTER X. 

In the time of Othonid, the Hebrew judge, Cadmus gave the art 
of writing to the Greeks. [Under tbe name of Hercules as under 
that of Apollo several distinct persons living at widely different 
periods are included.] Orpheus was a contemporary of Gideon. 

VOL.L g 



xcviu ANALYSIS OF THE ' OPUS MAJUS/ 

VOL. I. PAGES 

The Erythraean Sibyl lived between the taking of Troy and thc 
founding of Rome, in the seventh Olyihpiad, 433 years afterward. 
Hesiod, Homer's successor, is prior to the foundation of Rome. 
Romulus, Thales of Miletus, and Hezekiah were contemporaries . 49-51 

CHAPTER XI. 
With Thales began the series of the wise men of Greece; he 
himself was in Josiah*s time ; Pittacus, Solon, Bias and others, were 
contemporary with the Jewish captivity. Shortly afterwards arose 
the Italic school of Greek philosophy, Pythagoras at their head, in 
the time of the Jewish restoration; Tarquinius Superbus reigning 
at Rome 51-52 

CHAPTER XII. 
Pythagoras was foUowed by Archytas, Timaeus, and others ; but 
the great school of Greek philosophy, culminating in Aristotle, was 
inherited from Thales, through Anaximander, Anaximenes, Anaxa- 
goras, Archelaus, Socrates, and Plato. Plato, who travelled and 
studied in Egypt, and leamt much from the Pythagorean school, 
uttered truths so profound that many have thought that while in 
Egypt he must have been taught by the prophet Jeremiah ; though 
chronology will hardly confirm this view 52-54 

CHAPTER ,XIII. 
Aristotle studied under Socrates fbr three years, and for twenty 
years under Plato, whom he survived by forty-thrce years. He is 
the greatest of phik>sophers, rightly called The PhiJosopher. He 
strove by diligence and observation of nature to bring philosophy to 
the perfect state in which the patriarchs of old received it. But he 
was not infallible ; and as long as the worid lasts, additions to his 
knowledge will continually be made. Little use was made of his 
teaching till after the time of Mahomet, when Avicenna, Averroes 
and others brought it to light. Boethius indeed had translated 
some of his logical works. A great stimulus was given to the study 
of Aristotle by Michael Scot's translations, with commentaries, of his 
physical and metaphysical works. Of Avicenna^s commentaries, 
however, not more than a third part has yet been translated . 54-56 

CHAPTER XIV. 

The conclusion is that philosophy and theology are two aspects of 

one inseparable whole. Philosophy leads us to the threshold of divine 

truth ; apart from this function it has no meaning or value. But if 

rightly regarded its work never ends. In the sight of God we are 



PART 11. xcix 

VOL. I. PAGES 

but as children ever growing and leaming : what we know is due to 
those who have gone before us ; it is for us, if we are not dolts, to 
supply their shortcomings. As Christians it is our duty to avail 
ourselves of their teaching as the foundation of our more perfect 
doctrine, some glimpses of which, due to the tradition of the primitive 
patriarchs, were not denied to heathen writers .... 56-59 

CHAPTER XV. 
Such glimpses are to be found in the Sibyls, who prophesied of 
the death of Christ and of the last Judgement Divine truth, as 
Augustine has said, was not confined to the seed of Abraham. Job 
believed in the Resurrection 59-61 

CHAPTER XVI. 
There are two principles of metaphysic which will lead us to the 
same conclusion. The first is that the business of philosophy is to 
furnish a criterion of knowledge. It is aware of the incompleteness 
of its own knowledge in those matters which are of the greatest 
importance. It concludes from the goodness of God that such know- 
ledge must have been somewhere revealed : it finds this revelation 
in the Christian church ; and shows that Christian doctrine suppiies 
the complement to its teaching which hitherto had been wanting . 61-62 

CHAPTER XVII. 
Secondly, we must consider that all speculative philosophy has 
moral philosophy for its end and aim. The two are co-ordinated. 
As the speculative philosophy of antiquity is related to the moral 
philoBophy of that time, so must our own speculative philosophy be 
related to the moral philosophy of the Christian time, in other words, 
to Christian theology. But Christian ethic, as all authorities admit, 
assumes the previous existence of heathen ethic. So therefore must 
it be with the speculative philosophy of Christians. It starts with the 
speculative theories of antiquity and carries themmany stages farther. 
And in so doing the Christian theorist wiil not merely select from his 
heathen predecessors those truths the relation of which to theology 
is manifest. He will embrace all truths without distinction, arranging 
each in the division to which it belongs ; confident that all truth, in 
whatever department, will conduce in one way or another to that 
which is divine 62-64 

CHAPTER XVIII. 
We see then that wisdom was revealed in its fullness to the first 
patriarchs ; that, through the imposture of those who followed them, 



c ANALYSIS OF THE ' OPUS MAJUS/ 

VOL.I. PAGES 

it was afterwards hidden from men ; that Thales and his successors 
down to Aristotle, aided by some trace of primitive tradition, revived 
its culture. Phiiosophy, therefore, has its place in the divine govem- 
ment of the world : its conclusions must be demonstrated, diifused, 
and enlarged. It is a component part of that perfect wisdom which 
is contained in the Scriptures 64-65 



PART IIL 

THE STUDY OF LANGUAGE. 

Having seen the essential unity of wisdom as contained in 
Scripture, the canon law, and philosophy, we pass to the divisions 
of the subject. Tbese are five. The first is the study of grammar, 
not so much of Latin, as of the languages from which Latin received 
its culture. i. The quality of one language can never be perfectly 
reproduced in another. This is true even of the dialects of a language: 
far more true as between diiferent languages. A literal translation of 
Homer into Latin, and thence into a modem language, results in utter 
absurdity 66-67 

2. Secondiy, Latin is altogether wanting in many of the necessary 
words for the things described by foreign authors ... 67 

3. Thirdly, the translator must not only be perfectly acquainted 
with his subject, but aiso with the two languages with which he deals. 
Boethius and Robert Grosseteste fulfilled these conditions. But 
most translators have failed, and especially the translators of 
Aristotle. Jerome and Augustine have pointed out the errors 
of the Septuagint version and of the other versions. Nevertheless 
Jerome has left very many uncorrected 67-70 

4. Fourthly, in the Latin texts now in our possession there are 
vast omissions, as well as many confused and comipt passages. 
£. g. the third and fourth books of Maccabees are wanting : also the 
books of Samuel, Nathan, and Gad. We need also good translations 
of Josephus*s book of Antiquities, of many of the Greek fathers, of 
the second and third books of Avicenna, and of many essential treatises 
of Aristotle, on metaphysics, on physical and mathematical science, 
and on that part of his logic which deals with practical reason, the 
part that is of the greatest importance in the guidance of human 
life 70-73 

5. Fifthly, owing to our neglect of foreign languages, we fail to 
understand the allusions to them contained in many writings of 



PART IIL ci 

VOL. I. PAGES 

antiquity. We are told, for instance, that certain parts of the 
Scriptures are written not in Hebrew, but fii Chaldaean. The 
precise relations of these two languages ought to be made familiar 
tous 78-77 

6. Sixthly, the Latin text of the Scriptures, as commonly used, is 
extremely corrupt, and becomes more so as time goes on. It needs 
careful correction by reference to the original Greek and Hebrew. 
The versions in recent use by the Franciscans and Dominicans are 

far inferior to the old versions 77-81 

7. Seventhly, when the text is correct, there is often the greatest 
obscurity as to the interpretation. The same Latin word corresponds 
often to many totally distinct Hebrew words 81-85 

8. Eighthly, and lastly, since Latin grammar is formed on the 
model of Greek and Hebrew grammar, much confusion arises from 
this source. Latin words of foreign origin are not recognized ; and 
conversely, to many words of Latin origin a foreign source is 
erroneously given. Again mistakes occur as to the vowels and 
diphthongs in Greek that correspond to a Latin voweL The rules 
for gender that hold good in Latin are not applicable to Greek. The 
same holds good of pronunciation. The penultimate of possessive 
adjectives, which is long in the case of words of Latin origin, as 
bovinum, is short where they are derived from Greek, as in such 
words as crystallinum, adamantinum 85-92 

In condusion, I must point out the importance to the Church of 
linguistic studies ; (i) for explanation of the Hturgy, (2) of the formulae 
used in sacraments and consecrations, (3) for the due regulation of 
foreign churches, (4) for throwing light on the future history of the 
Church, (5) for intercourse with foreign nations .... 92-96 



PART IV. 

MATHEMATICAL SCIENCE. 

FlRST DlSTINCTION. 

CHAPTER I. 
I pass now to mathematics, the foundation and the key to all 
other sdences, studied from the earliest ages of the world, but of late 
fallen into neglect I shall deal successively with its application to 
buman knowledge, to divine knowledge, and to the govemment of 
thcChurch 97-98 



cii ANALYSIS OF THE ' OPUS MAJUS,' 

CHAPTER II. 

VOL. I. PAGES 

There is high authority for this estimate of mathematics. In the 
study of divine things and also of man's social life Boethias. and * 
Ptolemy show that it is of great service. The various modes of 
proportion have their analogue in civii polity. It is needed both in 
grammar and logic, as Alpharabius and Cassiodorus have shown. 
For prosody depends entirely on arithmetical relations. Logic, on 
its practical side, has the same purpose as poetic and rhetoric, which 
depend on harmony. Further, the subject-matter of logic is in- 
timately connected with mathematic. This is obvious in the 
Categories of quantity, of time, and of place. In the Category of 
quality much belongs to the mathematical domain, as e.g. geo- 
metrical form. The same may be said of the Category of relation. 
Spiritual substances can only be known through the medium of 
corporal : and the first step to the knowledge of body is the study 
of the heavenly bodies. The dependence of astronomy on mathe- 
matics is obvious 98-lOB 

CHAPTER III. 

We reach the same conciusion by reasoning. (a) In ail other 
sciences we use mathematical examples, because they illustrate the 
point without confusing complications ; e.g. in explaining the difference 
between augmentation and change, we add a gnomon to a rectangle, 
augmenting its magnitude without changing its shape. (b) Mathe- 
matical knowledge is innate in us and only needs drawing out, as 
Cicero explains, Quaest, Tusc, book i. ic) Mathematical truths 
are discovered prior to others. (d) They are simpler of compre- 
hension than others. (e) Students attain them who are incapable 
of proceeding further. (/) We see the same thing with children, 
who easily appreciate the simple arithmetical relations on which 
music depends. (g) We acquire our knowledge of things known to 
ourselves more easily than of things known to nature (i.e. intrinsi- 
cally simpler ; as, for instance, the truths of theology). But mathe- 
matics have the double character of being both relati vely and absolutely 
simpler. (h) In mathematics demons*ration is more complete: 
its cogency has the force of necessity, which is not the case 
either in physics, in metaphysic, in ethic. (i) In other sciences 
the uncertainty of the premisses involves uncertainty in the con- 
clusion. These principles require verification by some science more 
perfect than themselves: i.e. by mathematics. (k) Finally, the 
subject-matter of mathematics is more directly cognizable by our 
senses. It deals with quantity, which lies at the root of all know- 
ledge. The siroplest process of intellect implies continuous quantity, 



PART IV. ciii 

VOL. I. PAGES 

i. e. time. (/) Finally, we are confinned by the experience of all who 
have most distinguished themselves in science. They owe their 
results to the mathematical foundation of their studies . 103-108 



Second Distinction. 

CHAPTER I. 

Leaving method, and passing to the objects of study, we find it 
impossible to make progress without mathematics. The number and 
motions of the heavens, planetary motions, eclipses obvionsly requtre 
this science. And things terrestrial no less, since they are govemed 
by things celestial. The sun, acting on the surrounding medium, 
difTuses light. This may be taken as a type of the propagation, or 
multiplication, of species, or forces, by other agents. Let us consider 
how it takes place lOd-111 

CHAPTER II. 
Rays passing from a rarer medium to a denser, if they impinge upon 
the latter perpendicularly, pursue a rectilinear course. Otherwise 
they are refracted, i. e. diverted towards the perpendicular drawn to the 
surface of contact. In passingfrom denser to rarer they are diverted 
away finom this perpendicular. Hence if the denser body be spherical, 
the solar rays passing through it converge at a given point beyond it. 
The convergence of many rays produces heat. If the second medium 
is so dense that the * species ' cannot pass through, or at least that its 
transit cannot be appreciated by human vision, it is reflected. If 
the ray faHs perpendicuhir to this raedium, reflexion is in the reverse 
direction of incidence. If otherwise, the angle of reflexion is equal to 
the angle of incidence. By concave reflectors solar rays may be 
concentrated. If the reflector is spherical, those rays will be focussed 
which impinge on points in it corresponding to a circle placed at 
right angles with its axis. But reflectors can be devised of such form 
that all the rays shali fall on the reflecting surface at equal angles, 
and thus be reflected to the same focus. We have further to consider 
the diffusion of light impinging on objects not directly from the sun 
but indirectly. Constant exposure to direct rays would be destructive. 
Lastly, we have to consider the effect of light on the nerves of vision, 
when tbere is no question of its following any rectilinear course, 
its path being modi6ed by the vital principle 111-117 

CHAPTER IIL 

Rays issuing in tnfinite number Crom a point in every direction 
find their termination on hoUow surface of a sphere. Each point of 



civ ANALYSIS OF THE ' OPUS MAJVS: 

VOL. I. PAGES 

the surface acted on is the vertex of a cone of rays, of which the base 
is the whole surface of the agent 117-119 



Third Distinction. 

CHAPTER I. 

Light and other forces not merely propagate tbemselves by 
multiplication of species, but work ulterior effects ; light produces 
heat, heat putrefaction, putrefaction death, and so on. To these 
effects the same law applies. Rectilinear action is more effective 
than curvilinear; perpendicular than oblique. In refraction the 
effect is greater than in reflexion, because in the latter the reflected 
and incident rays neutralize each other. In refraction action is 
stronger where the second medium is denser than the first, because 
the ray is deflected towards, not away from, the perpendicular. In 
reflexion more is done by oblique rays than by perpendicular. With 
the latter there is neutralization of incident and reflected rays. 
Further, there can be but one perpendicular ray, but infinite numbers 
of oblique ; and these may all be made to converge . . . 119-123 

CHAPTER II. 

The rays of which a natural action consist form, as we have seen, 
a cone. In the shorter cones the strength of the action is promoted 
first by greater proximity of the agent, secondly by the greater 
proximity of the conterminal rays after intersection. On the other 
hand in the longer cones, the rays before intersection are the nearer 
to each other, and in this respect the action will be more potent. 
But the first of these conditions will outweigh the second . . 12S-124 

CHAPTER III. 

When two equal spheres interact, the half of each which is averted 
from the other is unaffected ; the extreme rays from each can only 
embrace the half of the other sphere. But with unequal spheres, the 
less receives rays from less than the hemisphere of the greater, which 
toucb more than its own hemisphere. From each point of a sphere 
rays issue into space outside of the tangent plane. Of these rays 
only one is perpendicular to the surface. This is the potent ray. 
Rays vertical to a sphere are diveigent. But when tbe object of 
vision is very remote, as in the case of stellar bodies, they appear 
to us to be parallel: just as the walls of a house seem parallel, 
although their lines of direction converge to the earth*s centre . 124-127 



PART IV. cv 

FOURTH DlSTINCTION. 

CHAPTER I. 

VOL.L PAGES 

6y the foregoing principles and others akin to them, which for 
want of space are here omitted, all natural actions are to be ex- 
plained. A few illustrations may be givcn. The planets receive 
their light from the sun. Hence when the earth is between the sun 
and moon, the moon is eclipsed by the earth's shadow. The cone 
of this shadow not reaching however to the other planets, these are 
not eclipsed. Again, that the eye and the stars can mutually transmit 
their emanations through the media of the planetary orbits, proves 
these media to be of great rarity, to be invisible, and non-luminous. 
The sphere of fire also is neither luminous nor visible. A planet 
differs from the sphere in which it moves by greater condensation of 
celestial substance; hence its luminosity. This, though ultimately 
derived from the sun, is not due to the sun's reflected rays. The 
difTusion of moonlight proves the moon to have independent 
luminosity. Owing to the magnitude of the sun being 170 times 
greater than that of the moon, much more than half of the earth is 
illuminated by the sun ; and the same is the case with the moon and 
planets. Other afTections of the moon's light depend on her varying 
conjunctions with planets and with constellations . . . 127-130 

CHAPTER II. 

The same principles may be applied to disprqye the alleged 
simplicity of cosmic structure. A star on the meridian is seen to be 
further from the pole than at its rising. In the latter position 
refraction displaces it. This shows the world to consist of distinct 
substances of varying density ; for a ray would not be refracted while 
passing through the same substance, even though its parts should be 
of different density 130-132 

CHAPTER III. 

Hence it is that the temperatures of the various zones are explained. 
Beneath the poles the cones of rays are prolo^ged, and therefore 
feeble ; capable only of raising vapours from the earth and sea, so 
that the air of those climates is heavy and cold, and unfit for living 
things. Nevertheless, owing to the length of the days and of the 
twilight in summer, the sun being never far distant, there may be 
places in those regions, favoured by the position and inclination of 
certain mountains, where the rays are so reilected that the climate is 
temperate 132-135 



cvi ANALYSJS OF THE ' OPUS MAJUS.' 

CHAPTER IV. 

VOL. I. PAGES 

Passing to the torrid zone, it would seem that the region under the 
equinoctial circle must be the hottest, since twice in the year the sun's 
rays there are vertical. But this is over-weighed by the fact that 
under the tropical signs the sun is nearly stationary. The matter is 
further complicated by the eccentricity of the solar orbit. . 135-137 

CHAPTER V. 

The emanations from the stars afTect not merely climate, but 
character; implanting on the new-bom child dispositions to good 
or evil, to quick or to dull apprehension : though free will, God's 
grace, temptations of the devil, or education may modify these innate 
tendencies 187-139 

CHAPTER VI. 

Our theory may be applied to the tidcs. Thcse evidently depend 
on thc moon. When thc rays fall obliquely on thc surface, their 
effea is only to raise vapours from the surface and create ebuilition 
and a consequent flow of water till the time comes whcn the rays fall 
vertically, and with force enough to extract the vapour ; and then the 
reflux begins. This however leaves it unexplained why the same 
thing happens in the hcmisphere averted from the moon. We must 
suppose the ninth or starry heaven to bc solid and impenctrable, and 
that the vertical rays of the moon are reflected from it, these 
producing the same efTcct as the incident rays .... 139-142 

CHAPTER VII. 

The application of these principles to the prcscrvation of life and 
health is obvious. Protection must be sought against the vertical 
rays of injurious emanations, as of the moon at night, of Satum and 
Mars, of persons infected with contagious disease, of the evil eye; 
and we must adapt our bodies to thc reception of emanations known 
to be salubrious . ^ 142 -U3 

CHAPTER VUI. 

\Vc may give mathematical disproof of what is one of the greatest 
errors in philosophy : namcly, that matter is of one kind only, the 
difTcrences of substancc resulting only from differencc in form. The 
consequcncc of this crror would bc to elcvate matter to equality with 



PART IV. cvii 

VOL. I. PAGES 

God. Nor is it enough to say that matter is infinite potentially, but 
not in essence. Nor that it is potentially infinite in the sense in 
whlch this is said of continuous quantity. For to attribute to matter 
existence in indefinite numbers of substances is to attribute to it 
infinity, not merely potentially» but in act. The contradiction in which 
this lands us may be set forth geometrically. Nothing infinite can 
have finite power, and conversely nothing finite can have infinite 
power 143-148 

CHAPTER IX. 

When two spheres are brought together, and the straight lines from 
their centres to the point of contact are continuous, the question 
arises whether these lines become one, or whether we are to 
regard them as two. Averroes maintained a distinction between 
mathematical quantity and natural quantity. But this distinction 
is untenable. The tines in question are two, although they have 
the efTect of one, and for convenience of speech may be spoken of 
as one. Against the separability of different masses of matter it 
is argued that if two circular planes are brought into contact 
and then separated, air will penetrate into the outer portion befbre 
the inner, hence for a moment there will be a vacuum in the central 
part. But the answer is that the separation is not simultaneous 
throughout the whole surfEice of the plane, so that the air penetrates 
gradually. From the divisibility of matter, it is not to be argued that 
the world is composed of an infinite number of material particles, as 
Leucippus and Democritus maintained. Were this so, it might be 
inferred that the diameter of the sqtiare was commensurable with its 
side ; which Eucltd in the seventh proposition of his tenth book has 
shown to be imposbible 148-152 

CHAFTER X. 

On geometrical grounds the shape of the universe can be inferred 
to be spherical. No other form would preclude the possibility of 
a vacuum in the course of its revolution. Cylindrical or lenticular 
form would suffice if revolution took place round a certain axis. With 
the spherical form revolution round whatsoever axis would avoid 
vacuum. Looked at from wtthin, it must be concave and spherical ; 
otherwise liaes drawn from the centre of the earth to the cxtremities 
of the universe would not be equaL Further, the sphere is that fomi 
which undcr a given surface has the greatest content. It is the . 
simplest and noblest of forms. The water, the air, and tbe fire 
surrounding the earth concentrically, are of similar form . . 152-157 



cviii ANALYSIS OF THE ' OPUS MAJUS/ 

CHAPTER XI. 

VOUI. PAGES 

Suppose two vessels similar in shape and equal in size ; one placed 
at a higher level than the other. More water can be placed in the 
lower, for its surface will be a portion of a smaller sphere: the 
diameter of the rim of the vessel being equal in both cases . 157-159 

CHAPTER Xn. 

The Platonic school maintained that heaven and the four elements 
corresponded to the five regular soHds. For there can be no more 
than five. Since in the dodekahedron the other fourcan be inscribed, 
this was regarded as representing heaven : fire was identified with 
the tetrahedron, air with the octahedron, earth with the cube, water 
with the icosihedron. But the difficuhy in this theory is that, 
though soiid masses can be built up of tetrahedra and of cubes with- 
out leaving vacua, this is not the case with the other three . 159-164 

CHAPTER XIII. 

There can be only one universe. For, on the supposition that 
there were two, both being spherical would touch in one point only, 
so that a vacuum would be left, which is impossible. Further, the 
universe cannot be infinite, otherwise two infinite lines, from one of 
which a given portion was cut off, would be equal ; i. e. the part 
would be equal to the whole, which is impossible . . . 164-165 

CHAPTER XIV. 

Unity of time does not imply unity of matter. Nor is it needful to 
suppose plurality of ages (aeva). The.subject of time is not matter, 
but motion. The subject of motion is not matter, but body composed 
of matter and form. Motion is of linear dimension. Prior excludes 
posterior, past excludes future. But as to the present being a point 
having no dimension, there is no such exclusion ; one point does not 
exclude another : many points occupy the position of one. One 
present moment suffices for all present moments. Hence time is one. 
And so to the conception of aevum the same applies. It is single and 
not multiple 165-167 

CHAPTER XV. 

In a body failing to the earth^s centre, a strain is involved : since, 
though the central point of the body tends directly towards the 
centre, the extreme points are prevented from doing so. From this 
strain heat resuits. This is shown by experiment to be the fact. But 
on geometrical grounds the reason of this fact appears; and our 
knowledge of it becomes thus more complete .... 167-169 



PART IV. cix 



CHAPTER XVI. 

VOL.I. PAGES 

When two eqaal weights are placed in the scales of a balance, and 
one scale isdepressed, the lower scale being nearer the earth's centre, 
wiJl have greater gravity. But this is counterbalanced by the 
tendency of the upper scale to fall in a curve of more rapid descent 
than the lower. The oscillation of the arms of the balance above and 
below the horizontal is due to the motion communicated to the 
surrounding air 169-174 



THE APPLICATION OF MATHEMATICS TO SACRED 

SUBJECTS 175-404 

We have now seen the potency of mathematics as applied to things 
secular. We now pass to its application to things divine. Philosophy 
is impossible without mathematics: theology without pbilosophy. 
All knowledge is contained, directiy or indirectly, in Scripture. 
Therefore for the right understanding of Scripture, knowledge of 
nature is needful. In Scripture there is a doubie meaning, literal 
and spiritual. The first is necessary for the second : and, as we have 
shown, mathematical knowiedge is necessary for it. It is certain that 
the patriarchs studied mathematical science and transmitted it to the 
Chaldaeans and Egyptians, whence it came to the Greeks. This is 
proved by Josephus, and confirmed by Jerome and other doctors, and 
also by such philosophers as Albumazar. Further, the fathers have 
themselves extoUed the value of mathematical science, as may be 
shown by passages from Cassiodorus, Augustine, Bede and others. 
The importance of mathematics to theoiogymay be considered under 
seven heads 175-180 

First head. Knowledge of the heavens. Astronomy shows 
the insignificance of the earth as compared with the heavens. The 
smallest of the stars is larger than the earth, and the largest star is 
insignificant compared with the space of the sky. The earth can 
be traversed at foot pace in three years. A star moving with immense 
veloaty takes thirty-suc thousand years to compass the heavens. 
Further, it is to astronomy that we look for solution of many theo- 
logical j>roblems, as for the substance of which the heavens are made, 
the position of paradise and of hell, the infiuence of heavenly bodies 
upon the things of earth. Again many obscurities in the text of 
Scripture can only be cleared up by astronomical research . 180-183 

The second head is that of sacred geography. By geography, 
which is dependent on astronomy, we can determine the precise 
position and the physical conditions of the places named in Scripture. 



cx ANALYSIS OF THE ' OPUS MAJUS/ 

VOL. I. PAGES 

All these, apart from their literal importance, have a distinct spiritual 
signification. The river symbolizes the world ; the Dead Sea, hell ; 
Jericho, the flesh ; the Mount of Olives, spiritual life ; the valley of 
Jehoshaphat, humility ; Jerusalem, the soul in the enjoyment of 
peace, or again the Church militant and triumphant. Minute 
research will reveal numberless intermediate meanings . . 188-187 

The third head relates to sacred chronology. Scripture presents 
to us a succession of times, with r^^d to which precise knowledge 
can oniy be given by mathematical astronomy. The starting-point 
is the creation of the world. Was this in the autumnal or the vemal 
equinox ? From what is said in the Old Testament as to the Feast 
of Ingathering [Exodus xxiii. 16] wc should infer the former. Yet 
Jewish and Christian commentators adopt the latter view. It will be 
for astronomy to decide this difficult point. P^urther, the question of 
the longevity of the ancient patriarchs has to be considered. One 
mode of accounting for it may be the more favourable position of the 
sun and the planets in primitive times. Again there is the problem 
of the Deluge. The right interpretation of Josephus points to 
November as the month in which it began. Lastly, did night come 
before day, or the converse? The former would seem to be the true 
view 187-195 

The fourth head deals not with chronology in general, but with 
the definition of periods. How is the beginning of a lunation 
tobe fixed ? by astronomical calculation, or by the moment when the 
new moon is visible ? The actual lunation is variable. The average 
lunation must be used. The Jews use the Metonic cyde of nineteen 
years, or 235 lunations. This gives twenty-nine days, twelve hours, 
and ^^iis of an hour for the mean lunation. They take a period of thir- 
teen lunar cydes or 247 years, within which all their festivals recur at 
the same moment. The lunation is considered to begin with the sun- 
set immediately foUowing the computed time. These considerations 
may be applied to the date of the Creation, of Noah*s issue from the 
ark, of the Passover, and finally of the Passion. The current belief 
in the Latin Church is that Christ was bom in the second year of 
a lunar cycle. and died on March 25 (a. d. viii Kal. AprilisS themoon 
being at the fifteenth day (the Greeks holding that it was the 
fourteenth day). Against this much may be urged. It implies that 
it was in the thirteenth year of a cyclc. From the computation of 
S. Dionysius this would involve the Passion taking place on a Sunday, 
which is impossible. A table is appended showing one solution of the 
difficulty. This wouid show the date of the Passion to be April 3 
(a. d. iii Non. Aprilis), on the fifteenth year of the lunar cycle, Christ 
being tben thirty-two years old. This view is ofTered to the Pope for 
consideration 195-210 



PART IV. cxi 

VOL. I. PAGES 

Fifth head. This reiates to geometrical forms; and again it 
has to be premised that the spiritual meaning of Scripture is not 
to be grasped, unless the literal meaning be first understood. The 
precise form of the ark, the tabemade, the temple should be pre- 
sented to us with mathematicai accuracy ; it will then be possible to 
interpret their mystical signification. A remarkable case in point 
is the rainbow, of which we are told that it is a symbol of God's 
promise as to the Deluge. The meaning of this is misunderstood 
for want of understanding the geometry of the lainbow, which is 
produced by the solar rays striking on the raindrops and being 
refracted or reflected thence. Only by geometry can such a text 
as that of the threefold buming of mountains by the sun be under- 
stood. The mountains receive direct rays. The rays reflected by 
them are focussed in the air and contribute to warm them. Lasdy, 
there are the doubly refracted rays passing from the sun into the 
clouds and from the clouds into the air. Again» the rays may fall 
either vertically, or obliquely, or horizontally, producing different 
effects in each case. The laws as to the passage of light through 
space apply equally to the passage of all other forces. Of all these 
things there is a spiritual interpretation. Direct vertical rays may 
be compared to the action of grace on the righteous ; they neither 
reflect nor refract it. In the wicked we see the light driven away, 
reflected : in the imperfect it is bent aside, refracted. It is to be 
noted here that the geometrical form of the triangle is speciaily 
adapted to symbolize the Trinity. Each angle is distinct yet each 
embraces the whole space. Again, our geometrical principles as to 
the action of forces may be applied to the estimation of the forces of 
temptation, which act in proportion to their proximity. Hence the 
need of keeping the tempted as far removed as possible from the 
objects which tempt 210-219 

Sixth bead. This relates to number. (a) As with geometrical 
forms, so with number there is a spiritual meaning behind the literal 
meaning. (b) For the understanding of chronicles it is necessary to 
know the different systems of numeration, and to be able to convert 
one into another. (c) There are various arithmetical operations in 
the Jewish law requiring a knowledge of the subject. (d) There are 
many corruptions in the text which only an arithmetician can unravel. 
{e) llie perfections inherent in the number three can only be under- 
stood by arithmeticians. (/) Arithmetic is necessary in astronomy, 
which we have seen to be needful to the theologian. Some instances 
of its value in astronomy are here given. We have to define the 
length of a line on the earth's surface corresponding to a degree. 
We must take a mile as 4,000 cubits : a cubit as \\ feet. Howmany 
miles must we walk northward from a given point to find the pole- 



cxii ANALYSIS OF THE ' OPUS MAJUS/ 

VOL. I. PAGES 

star a degree higher in the sky? We shall find the result to be 
fifty-six miles, 2,984^^ cubits. From the diameter of the earth we 
obtain its circumference and its surface. The distance of the heavenly 
bodies may be measured in semidiameters of the earth =3,250 miles. 
Alfraganus estimates the distance of the starry sphere to be 20,110 
semidiameters ; which gives the diameter of this sphere as 
130,715,000 miles. From this we can calculate the circumference 
and surface. The longest distance of Saturn is the semidiameter of 
this sphere, or 65,357,500 miles, of Jupiter 46,816,250 miles, of Mars 
28,847,000 miles, of the Sun 3,965,000 miles, of Venus 3,640,000 miles, 
of Mercury 542,750 miles, of the Moon 208,541! miies ; the shorter 
distance of the preceding planet being always equal to the longer 
distance of the succeeding. As to the ninth and the tenth heaven we 
have no scientific knowledge. As to the height of the atmosphere there 
is great uncertainty. For measuring the apparent diameters of the 
Sun and the Moon recourse has been to water-clocks ; the number 
of drops issuing from the beginning to the end of the Sun's rising 
have been compared with the number issuing during a revolution 
of the heavens. But there are more accurate methods by astrolabes 
or quadrants. From these, and from observations of eclipses, the 
moon's diameter is estimated at f^ of the £arth's diameter. The 
Earth is theref^re about 31} as large as the moon. Similarly the 
Sun will be found to be 170 times as large as the Earth. Mercury is 
■^^js of the Earth. In a similar way the relative magnitude of 
the other planets as compared with the Earth may be determined. 
The fixed stars are 1,022 in number, and are divided into six groups 
according to this magnitude. Those of the first magnitude are 107 
times as large as the Earth ; of the second, ninety times the £arth's 
magnitude : of the third, seventy-two times, of the fourth, fifty-four 
times, of the fifth, thirty-sbc times, of the sixth, eighteen times. But 
besides these there are infinite numbers of other stars whose 
magnitude cannot be determined 219-236 

Seventh head. Music. The theologian should be acquainted with 
the theory, if not with the practice, of vocal and instrumental music. 
Music covers the whole ground of recitation, punctuation, accent, 
things necessary for prose as well as poetry. Of instruments again 
many are spoken of in Scripture, ancf each has a spiritual as well as 
literal meaning. Nor must dancing, which may be called visible 
music, be forgotten 236-238 

We have now to consider certain objections that have been raised 
with regard to mathematical science. Mathematic has been con- 
founded with magic, and put on the same level as fortune-telling, 
witch-craft, and the preparation of charms and incantations. It has 
been credited with the doctrine that human actions are absolutely 



PART IV. cxiii 

VOL. I. PAGKS 

detennined by stellar influences. But this doctrine is explicitly 
condemned by all philosophers,.both of Greece, Rome, and Arabia. 
They maintain free-wiU against any such supposed physical necessity ; 
and they reprobate utterly the use of charms and incantations. The 
prejudice .against mathematics was strengthened by the strife of 
heathenism against Christianity, in which magic was used by the 
former, and in wbich Christian miracles were accouoted for by magic. 
The reproach of denying free-will remained, when the suspicion of 
magic had passed away. But examination of Ptokmys works shows 
clearly that he never fell into this error. He, and his principal 
Arabian commentators, held that the forecasts of the future revealed 
by astronomy indicated general tendencies only, and did not impose 
any specific compolsion on individual actions. But this distinction 
has not been always perceived in the attacks made by Christian 
wri^ers on mathematical science. They have confounded true science 
withfalse 238-249 

What is true is that the influences of the stars implant certain 
tendendes to good or evil action, always at the same time leaving free 
scope to human will. It is evident that physical temperament is one 
of the factors in human action. Temperament is itself a result of the 
intluence of the stars. That dimate affects character is obvious to 
every one. And this influence is to be traced in minimis. From 
every part of the sky to every point of the earth's surface a cone of 
forces proceeds, aflecting more or kss every community and every 
individual, though not in such a way as to override free-will. These 
things would be studied by physicians if they were better acquainted 
with astronomy. In the case of a commonwealth, or of the states- 
men who direct commonwealths, it is more easy to discem the 
nature and degree of such influences, and to forecast thdr re- 
sults. And great advantage will accrue - to the community from 
doing 80 249-253 

We now arrive at the practical applications of mathematical science 
to Church govemment. The first of these is the proof offered by 
astrology of the superiority of Christianity to other religions, and 
the insight given into the nature'of Antichrist. It must be under- 
stood that the heaven is to be divided into twelve Houses ; that is, 
taking the quadrants formed by the intersection of the meridian 
and horizon, each teay be divided into three. To five of the 
seven planets two Houses are allotted ; to Mercury and the Moon 
one . each. The association of Jupiter with each of the other 
planets has a spedal meaning. If with Satum, the reference is to 
Judai^m. With Mars, to Chaldaeism. With the Sun, to Egyptian 
leligioo. With Venus, to the Saracen wofship. With Mercury, 
to Cbristianity . . . . . . . . . 253-25^ 

VOL. I. h 



cxiv ANALYSIS OF THE ' OPUS MAJUS/ 

VOL. I PAGRS 

But there is another and more essential meaning of the ynmd 
House. If we divide the ecliptic into twelve parts, and through the 
divisions conduct drdes intersecting at the poles of the ecliptic, 
tlie regions between any two of these circles is in the true sense 
a House; bearing the name of its zodiacal sign. The principal 
House of each planet is that in which it was created. Leo is the . 
House of tbe Sun, Capricom of Satum, Sagittarius of Jupiter, Vii|ro ' 
of Mercury. There are certain signs for each planet which are 
called its Exaltation ; for the Sun Aries, for Satura Libra, for Jupiter 
Cancer, for Mars Capricora, for Venus Pisces, for Mercury Virgo. 
The signs are divided iato four groups : three, Arie9> Leo, Sagittarius, 
are hot and dry : three» Tauras, Vii^^ and Capricora, are cold 
and dry : three, Gemini, Libra, Aquarius, are hot and moist : three, 
Cancer, Scorpio, and Pisces, are cold and moist. A planet being 
in any of the groups to which its House bdongs is said to be in its 
Triplicity. We have further to consider Boundaries and Aspects. 
With regard to Boundaries, they vary for each planet and for each 
sign. With regard to Aspects, each sign is divided into three equal 
portions of ten degrees, and a portion is assigned to each planet in 
sequence 258-261 

It will appear in the result that Mercury has manifold and strong 
connexions with the sig^ of Virgo. As Mercury is connected with 
Christian faith, so is the Moon, with its irregular motions, connected 
with the corruption of that faith. The conjunctions of the planets, 
and especially those of Jupiter and Satura, throw light on important 
epochs of history. These are of three kinds, occurring respectivdy 
in periods of 20, of 240, and of 960 years. Judging from what took 
place at previous periods, it may be inferred that the Mahometan 
faith will not be of much longer duration. There yet remains the 
period of Antichrist; on the date of which study of these astronomical 
periods may throw light 261-269 

A second application of mathematics to the service of the Church 
is the correction of the Calendar. The Julian Calendar fixed the 
length of the year at 365} days. Hence the arrangement of an 
additional day every fourth year. But this estimate is known to be 
too great by the j^ part of a day. Therefore in every 130 years 
there is an accumulated error of one day 269-271 

Again, it has been assumed that the equinoxes and solstices 
occurred on fixed days. These days in the beginning of the Church 
were fixed thus: the winter solstice on December 25, the veroal 
equinox on March 25, the summer solstice on June 24, the autumnal 
equinox on September 24. Subsequently the vernal equinox was 
transposed to March 21. Hence the earliest Easter, being the flrst 
Sunday after the full moon sucoeeding to the vemal equinox, was 



PART IV. cxv 

VOL. I. PAGKS 

March 22. But the winter solstice and the vemal equinox are no 
longer on these days. At the present time the winter solstice is 
on December 13, the vemal equinox on March 13, the summer 
solstice on Jnne 15, the autumnal equinox on September 16. In 
every 125 years the error of another day accumulates. The con- 
sequence of this error is that Easter is observed at the wrong 
time, in the third and in the fourteenth years of the lunar cycle. 
The error will be iaot more serious in futuxe centuriies, so that 
ultimately the period when Lent should be observed will be at a 

time when every one is eating meat 271-274 

Further, there is a serious error in- the computation of tfae lunar 
cycle. Successive periods of nineteen years differ in length, some 
containing ibur, others iive leap-years. The only* satisfiEictory period 
would be thirty Arab years of twelve lunations, making 10,631 days. 
It is tnie that the Council of Nice adopted the lunar cycle; and 
120 years afterwards it was confirmed by Pope Leo» The error at 
this latter period was not more than a day. Since that time astro- 
nomy has been in disrepute, for reasons already mentioiied, aiid no 
one has been found who could clearly indicate the error, with 
suflficient authority ; although in the time of Pope Hilary some con* 
sideration was given to the subject. At the present titne the error 
is so great as to attract the ridicule of Jewish and Arab astronomers, 
and deserves the serious attention of the ruler of tfae Church • 275-285 



Geography. 

We now pass to the influence of the heavens upon things terrestnal. 
In allthings that are brought forth on earth, whether forgood or evil, 
the sun and the heavens are the moving cause. We have therefbre 
to consider the diflTerent ways in which different parts of the earth's 
surface are aflfected by these agencies. Imagining that suifEice 
divided by the equator and the equinoctial colure into four equal 
portions, we have specially to consider the portion contained between 
the equator and the poles, bounded east and west by the colure. 
What proportion does land bear to water ? Ptolemy thought one- 
sixth, but other authorities think the proportion mucfa greater. 
Seneca and Pliny look on the space of ocean dividing the west of 
Spain from the east of India as inconsiderable. Under the word 
Spain we must include a vast tract extending westwards across the 
Straits of Gibraltar, in tbe direction of Atlas. On the whole, it seems 
probable that the land known to us from east to west extends over 
more than half the eartfa'8 drcumference. Further, it seems probable 

ha 



cxyi ANALYSIS OF THE 'X)PUS MAJUS/ 

VOL. I. PAGES 

that the disposition of land and water may be similar on the otfaer * 
side of the northem hemisphere to that of this side ; and the same 
may be argued of the two divisions of the soutbem hemisphere, 
especially as the sun in its annual course comes nearer to it • 286-294 

Speaking of the parts known to us, Ptolemy and others have dis- 
tinguished seven r//ma/a— marking them by the increasing length 
of the longest day. The position of each place referred to is defined 
by the intersection of the line of latitude and longitude belonging 
to it. The zonesi or dimaia^ of Ptolemy are marked according to the 
•increase of a quarter of an hour in the length of the longest day up 
to the sixty-first degree of latitude ; thence to the sixty-fourth degree, 
by half an hour*s increase ; thence to the sixty-sixth by one hour^s 
increase. Peyond this point we come to the region where in the 
summer season the sun is always abovethe horizon, in winter always 
beneath it. Here the divisions must be marked according as the 
longest day is one month, or two or three, up to six. As to iongi- 
tude, it should be measnred not from any arbitrary point, but frdm 
the true east and west on the equator. The neglect of this pre- 
caution has led to much confusion in the tables of Toledo ; and 
generally a far more accurate determination of the latitude and longi- 
tude of towns and states is needed, such as can only be instituted by 
apostolical, imperial, or at least regal authority .... 294-801 

A right understanding of locaiity and climate concems alike the 
interpretation of Scripture, the propagation of the faith, and the wel- 
fare of commonwealths. Missionaries in particular should know the 
distribution of the various religions of the world ; where the lost 
tribes of Judea are to be looked for, where the incursions of Anti- 
christ are most to be dreaded. Our knowledge of these matters, 
derived from Pliny, Ptolemy and other writers of antiquity, has been ^ 
recently enlarged by the travels of WiUiam Rubruquis in Central 
Asia 301-805 

At the tropic of Cancer we begin to find regions where the sun at 
the summer solstice casts no shadow. Southwards to the tropic of 
Capricom the same phenomenon occurs for each place twice in the 
year. And we have knowledge of regions south of the tropic of 
Capricom where the noonday shadow is always to the south. And 
though in these last the sun approaches so nearly at our winter time, 
and recedes so far at our sununer time, as to involve great extremities 
of heat and cold, yet these evils may be lessened by the configuration 
of mountain and plain, so that the region is habitable, as we know 
in the.caseof the island of Taprobane 805-809 

We may begin our description of the habitable world with India. 
Its southem coasts are washed bya branch of the AUantic Ocean, so 
vast;that from the mouth of the Red Sea to the south of India is . 



PART JV. cxvii 

■ VOL. I. PAGKS 

a year^s voyage. India has a third of tfae habitable surfiace. East of 
Soutb India is the tsland of Taprobane abounding in gold and jewels, 
and govemed peaceably by an elected king with a council . 309-810 

The south coast of India passes from the south tropic north-west, 
cutting the equator at Aryni, a point ninety degrees from the west, 
but more than that Hrom the east Then the coast line proceeds 
south-west, pasding the opening of the Red Sea, and bounding South 
Ethiopia till the Indian Sea joins the Atlantic On the Nile, at the 
latitude of sixteen degrees, we find the isiand of Saba, the royal city 
of Aethiopia— called also Meroe, about 700 miles from the coast. At 
the same latitude, on the Red Sea, is the city of Ptolemais. Between 
thesetwo, or more probably to the west of Meroe, is Berenice the city 
of the Troglodytes, who are identified with the Garamantes. West 
of these are the Hesperi 810 313 

Egypt is the region tncluded between Syene and the Mediterra- 
nean : divided into upper Egypt or the Thebais, and the Delta. 
Tlie Delta extends from Heliopolis on the Arabian frontier to 
Alexandria on the confines of Africa. Africa received its name 
from AfTer, a descendant of Abiaham. Before this it had been called 
Libya. Much of the northem coast was ocaipied by Medes, 
Persians, and Armenians brought by Hercules. The interior was 
occupied by Gaetulians, afterwards called Numidians, amongst whom 
the Carthaginians established their empire. Between Carthage and 
Egypt are Tripolis and Cyrene 318-318 

So-nething must be said of the Nile. Its origin is in Aethiopia, 
probably in the regioh bordering on the Red Sea. Its course is for 
a long ttme westwards as far as Meroe. Between Meroe and Syene 
it is northward, and so onward to the Delta. Its inundation is in 
sununer. henoe the difficulty of explaining it. The opinion of Thales 
that it was due to northem winds preventing the outflow, is disproved 
by the fact that the inundation begins in the upper part of the river. 
A more probable view is that of Anaxagoras, that it is due to the 
melting of snow in the mountatns of Aethiopia. Aristotle rejects 
this vieu% but gives reasons for supposing a great lainfall to occur 
n summer time in the marshy regions from which the Nile 
flows 318 825 

The region from the eastem bank of the Nile is to be regarded 
as part of Arabia, which also includes the vast space eastward as 
far as the Persian gulf and northward through south and east 
Palestine as far as the Euphrates. We can ik>w trace the principal 
positions of the Hebrews in the Desert, and also of Edom, of Moab 
and of other neighbouring tribes mentioned in the Scriptures . 325-382 

The region between the Tigris and the Euphrates is Assyria or 
Mesopotamia, in wfaich were the cities of Ninevefa, Aram, and 



Cxviil ANALYSIS OF THE ' OPUS MAJUS/ 

VOL. I. PAGES 

Babylon. In Babylonia dwelt Noah and his sons after the deluge. 
Both the Tigris and the Euphrates rise in Armenia. The Tigris 
fiows for some space underground before reaching Nineveh and 
joining the Euphiates. The Euphrates swells in summer as does 
the Nile. To the east of the Euphrates lie North Arabia and Syria, 
the sottthem part of which is the Holy Land. Here a more detailed 
description becomes necessary ....... 332-335 

Beginning with the coast, we find Gaza on the confines of Egypt 
and Palestine, then proceeding northward Ascalon, Joppa, Azotus, 
Caesarea, Acon, Tyre, Sarepta, Sidon, Barut, Gibeleth, Tortosa, 
Laodicea. From this last to Antioch is two days' joumey. From 
Antioch to Tarsus in Cilicia three days' joumey . . . 335 336 

Passing to -the intcrior, we find Beer-sbeba at the southem 
lx>undary. Twenty miles to the north is Hebron, the place of 
sepulture of the patriarchs. Near Hebron is Carmel, and a little 
to the east, the town and mountain of Ziph ; fourteen miles to the 
north is Bethlehem, which is six miles to the south of Jerusalem. 
This city is twelve leagues from Joppa, and nine leagues to the east 
of it is Jericho. Tekoa, the country of Amos, is twelve miles to the 
south-east, and here we come to Pentapolis, the region of the Dead 
Sea, where nothing lives, where bodies that usually sink in water 
float, lumps of bitumen are found on the surface ; here too are found 
the apples of Sodom 336-339 

The Jordan flows into the Dead Sea. Its origin is by two 
branches from Lebanon, and it passes through the lakes of 
Gennesareth and Tiberias. North of Jericho is Scythopolis or 
Bethsan. Westward and to the north of Jerusalem is Anathoth 
the birthplace of Jeremiah. Thence northward, twelve leagues from 
Jemsalem, is Samaria, now called Sebaste. North-eastward is the 
plain of Megiddo ; north of this and east of Acon, at seven leagues* 
distance, is Nazareth. Two leagues further east is Mount Tabor, 
and the city of Tiberias, and the lake of that name, containing the 
purest waters of Judaea ; it is near but distinct from the lake of 
Gennesareth. To the north, separated by a desert region, are 
Bethsaida and Capemaum. East of Acon, and two leagues north 
of Nazareth, is Cana of Galilee. Still further north is Corazaim. 
We are thus brought into the region of Lebanon, whence fertilizing 
waters descend to the neighbourhood of Tyre and Sidon . . 339-343 

Beyond Jordan, north of the Dead Sea, is the citadel of Macheron. 
Here was thc tribe of Reuben. North is Pella, at the boundary of 
Palestine on that side of Jordan. Eastward were the kingdoms 
of Og and of Sihon. On their boundaries is Ramoth-Gilead, not 
far from the range of Anti-Lebanon. In this neighbourhood is the 
city of Damascus, situated four days' joumey from Jerusalem • 343-344 



iPART IV. cxix 

VOL. I PAGBS 

Suimning upthese details, we may speak of Syria as indudiBg the 
space from the Euphrates to the Mediterranean, and from Cilicia to 
Egypt. It .is divided into the provinces of Syria Comagena, Syria 
Caeley Phoenictan Syriaf and the thrce divisions of Pakstine, Galilaea, 
Samaria and Judaea. Comage is the capital city of the first, 
Antioch of the second. Phoenician Syria extends from the south of 
Lebanon to the novth of Palestine. It -contains the cities of 
Damascus, Tripolis, Tyre and Sidon ; and beyond 'the* Jordan, 
Pella and Mount Hennon and Mount Gilead .... 344-347 

The three regions of Galilaea, Samaria, and Judaea belonged to 
the Hebrews, who held the region beyond the Jordan from the 
Dead Sea to Mount Hermon. In the north part of Galilee is 
Decapolis. South of this Ithuraea or the tetrarchy of Trachonitis. 
The northem part of Galilee contained a mixed race of Jews and 
heathen. Lower Galilee begins with the lake of Tiberias. South 
of Galilee is the district of Samaria, and south of SanKaria is 
Judaea . 347-348 

We see then that the amount of territory possessed by the Jews 
was but small. Fiom Dan to Beer-sheba is but 170 miles, from 
Joppa to the Jordan, not seventy. To this, their possessions east 
of the Jordan are to be added . 348-350 

Passing toother regions of the world, we find the range <of Mount 
Taurus extending from the Indian Ocean, separating Parthia, 
Mesopotamia, and Syria, from the Scythian regions, and from 
Armenia and Cappadocia, and finally reaching Cilicia. In its 
course' this range leceives various names, as Caucasian, Caspian, 
Hyrcanian and many others. Media, Persia, Parthia, lie between 
the Indus and the Tigris east and west, having the Caspian Sea 
and Caucasian mountains to the north, and the Persian gulf to the 
south. The Parthian empire coincides with what was once the 
Persian 350-352 

India lies east of the Indus, bounded on ihe north by the Seric 
sea and by the mountains which extend east from the Caucasian 
range. Vast as the Indus is, the Ganges flowing from the Caucasus 
into the Eastern Ocean is yet greater. On the Ganges live the 
Brahmins, living a life of extreme temperance and chastity, and 
attaining great longevity. North of India is the Scythian ocean and 
the Caucasian range already spoken of 352-353 

Westward from India, at the confines of India and Parthia, we 
find the Caspian gates on the south shores of the Caspian or 
Hyrcanian Sea. This sea is entirely inland, formed by great rivers 
flowing from the north. West of Parthia is Hyrcania, and then the 
greater Armenia divided by the Euphrates from Cappadocia. The 
lesser Armenia is identified with Cilicia. This r^on from south to 



clcx ANALYSIS OF THE ' OPUS MAJUS/ 

VOL. I. PAGES 

north is of about four days* joamey, bounded by Lycaonia, now 
called Turkia, and induding se^^cral ancient provinces as Lydia and 
Phrygia. The wbole of this country is now called by the Greeks 
' Anat(riia, otherwise Asia Minor . 353-856 

Dividing this from Europe is the Artti of St. George, with Constanti- 
nop]e on its left shore, leading to the Pontic Sea, which extends 1,400 
miles froni east to west. From north to south its narrowest part is 
between Sinopolis and the province of Cassaria (Crimea), on the east 
of which is the. shallow sea of Maeotis formed by the mouth of the 
Tanais (Sea of AsoQ. This river flows from the Riphaean mountains 
in the extreme north. From the Tanais to the Danube is a vast 
desert plain, which it takes the Tartar horsemen two months to 
traverse. It is bounded by Poland and Hungary. To the north of it 
is Great Russia— bounded to the west by the Baltic Sea, beyond 
which lie Denmark, Sweden, and Norway. Then across a great 
expanse of sea Scotland and England lie to the west, and beycnd 
them Ireland 856-358 

At the north of the Baltic Sea is Esthonia, eastward is Livonia, 
and south of it Courlandia, then Prussia and Poiherania. On the 
confines of Dacia and Saxonia is the port of Lubec. In the Baltic 
)ies the island of Gothland. South of Prussia is Poland ; south of 
this Bohemia, then Austria ; west of Austria is Alemannia, France and 
Spain ; eastward is Hungary bounded to the ncnth-east by Albania, 
which extends as far as the river Don, having Bulgaria, and Con- 
stantinople, and the province of Cassaria to the south, and Russia 
to the north. North again of Russia are the Hyperboreans, a peaceful 
long-lived race, with a climate far more equable than might be ex- 
pected from its position. Among these northem nations is a great 
variety of religions. The Livonians, Curlandians, Prussians, Estho- 
nians are pagans. The Ruscenes are Greek Christians, though in 
common with the Poles, Bohemians and many others, their language 
is Sclavonian. The Tartars, who have subjugated almost all nations 
from the Danube to the extreme east, lead a wandering pastoral life. 
Some of the tribes subject to them are pagans, others follow the 
Mahometan law 358-361 

On the north-eastem border of the Pontic Sea is the land of the 
Georgians, and Corasiminians, where of old Amazons u^d to live. 
South of these are Cappadocia and Armenia. From the mountains 
of Armenia fiow thc Euphrates and Tigris. Here Noah*s ark rested. 
SS. Bartholomew, Judas, and Thaddeus suffered martyrdom here; 
and at one time there were 800 Christian churches ; though Rubruquis 
found but two, and these small. Tbe city of Naxuana, the principal 
town of Armenia, now destroyed by the Tartars, was visited by him, 
as he passed up the river Araxes. In the mountains to the east he 



PART IV. cxxi 

VOL. I. PAGES 

found the Alani who are tolerant and orthodox Christians, and east 
ofthese the Lelgi who are Saracens 361-364 

This brings us to the southem shore of the Caspian Sea, where 
Alexander erected the Caspian gates, as a protection against the 
incursion of barbaric tribes from the north. Rubruquis passed 
through these gates. This being the region of Gog and Magog, 
who after ravaging the world will become at last the foes of Anti- 
christy it is of the highest importance to the Church that its geo- 
graphy should be known. The Caspian Sea, extending from west 
to east, is as large as the Pontic Sea, and to compass it is a four 
months* joumey. Rubmquis tniversed its northera shore in going 
to the Tartar emperor, and its westem shore in retuming. It has 
no connexion with the ocean, being formed by the Ethilia (Volga) 
and other rivers. From the Don to the Ethilia was the land of 
old called Albania, till lately occupied by the Cumani. East of the 
Volga also the Cumanians dwelt till dispossessed by the Tartars. 
Northward is Asiatic Bulgaria, whose inhabitants are of the same 
race and language as those on the Danube. East of this region is 
the land of the Huns 364-367 

These regions extend as far as Caracathaia or Black Cathay. 
Here tt is that the emperor of Tartary dwells, changing his abode 
according to the season. It has sometimes been said that Prester 
John lived here, but his kingdom, formed of a Nestorian tribe, was 
far more westerly. His power was established on the death of Coir 
Cham. Prester John was succeeded by his brother Unc, who took 
the title of Cham, and who reigned for a time in Cara Coram, the 
principal Tartar city. But Unc Cham was destroyed by the Tartar 
leader Chinghis. His grandson, the son of Unc*s daughter, is Mangu 
Cham to whom Rubmquis was sent by the King of France. The 
name given to these Tartars by themselves is Moal. They have 
by this time conquered nearly all Asia ; they hold Russia, Bnlgaria, 
and the neighbourhood of Constantinople 367-371 

Eastward of Black Cathay are several tribes with peculiar habits ; 
and beyond them, to the extreme east, is Great Cathay, the nation 
of the Seres, whenoe comes silken dothing. The inhabitants of this 
country are skilful workmen, and acquainted with the medicai 
properties of plants, and carefully study the changes of the pulse 
and othcr symptoms of disease. They use paper-money. They are 
for the most part idolaters (Buddhists) ; but Saracens are mtxed with 
them, and also Nestorians, who preach and practise a cormpt form of 
Christianity. Their patriarch professes willingness to acknowledge 
the authority of the Roman See. Of these various peoples some write 
from above downwards and from right to left. Others write as we 
do^ and with our letters. The mhabitants of Eastem Cathay paint 



cxxii ANALYSJS OF THE * OPUS MAJLS/ 

'*' "' VUL. I. PAGES 

rather than write. forming groups of letters, each group repreaeniing 
a sentence. The gepgraphy of Westem Europe does not require any 
detailed description .. .. .. . 871-376 



ASTROLOGY. 

This geographical description should be followed by an account 
which I have not been able to complete, {a) of the stars, (b) of the 
pianetSy (c) ofthe way in which the climatic disposition of each place 
is affected by them, {d) thus making true astrological judgements 
possible, (e) with the resuU of promoting the safety of the state. All 
that I can do is to offer a few remarks on these points. Each of the 
tixed stars has properties of its own. Those of the twelve signs are 
specially important to us. A spectal treatise would be needed to 
describe these characteristics adequately and to point out the way 
in which we are affected by them. Each planet has also its special 
character, modified by the zodiacal sign in which they are situate, by 
their aspects, that is by any two or more of them being in the same, 
in opposite, or in intermediate directions, by the position reached in 
their epicycle or eccentric, and bythe House of the heavens which 
they may be occupying. This again requires a special treatise- 376-379 

From this we pass to the effects.produced by the heavens on places 
and thingsupon the earth. The sun may be said to beget no less 
than the parent : and the sun'sinfluence endores through life. JElach 
spot on the earth's surface is the centre of a distinct horizon, and is 
thus affected differently from every other. We have to consider its 
distance from the pole and the equator, what stars are in the zenith, 
and what signs are dominant there. On all these points the Hebrew 
astronomers are specially instructive. Special parts of the body are 
affected bydifferent constellations, and by the position of the moon 
in them. Each hour of the day is under the control of a particular 
planet. On medical art especially, but also on allother departments 
of human activity, the bearing of all this is obvious. The quarters 
of the moon must be of course studied, and also the daily transit of 
the moon through a portion of theZodiac 379-385 

Besides the revolutions of the moon and sun, .attention must be 
given to those of the planets, especially to those of longer period. 
The comct for.instance of 1264 was due to Mars, and was related to 
the wars in England, Spain, and Italy of that time. All planetary 
conjunctions are important; but of special importance to man*s 
welfare are the conjunctions of the Moon with stars of various nature. 
Position in the orbit must always be cxamined. In the apsis 
planetary force is greatest: weakest in the oppo&iie point. We 



PART IV. cxxiit 

VOL. I. PAGKS 

must observe too in what house each plaaeC may be; lor on tfais 
the whole complexion of the year may largely depend. On the 
foregoing data we form our judgements of events past, present, and 
future. As a first step to this we must form accurate astronomical 
tables exhibiting the position of the heavenly . bodies at any given 
date. Comparing these positions -with the political events of such 
a date, we obtain methods for forecasting ftiture events. Our best 
authorities on this subject are Albumazar, Ptolemy, Haly, and the 
Hebiew astrologers. A work of Aristotle on celestial impressions 
should also be translated 385-390 

Next comes the question, How far can this knowledge guide our 
action ? We cannot do away with the force resultin^ from any 
special position of the stars: but we can modifyour own action so 
as not to be adversely aflected by it. If we know that great cold 
is coming, we can make provision against cold. Similarly the 
trained astronomer will provide against pestiience, or any other 
calamity which he sees impending. *Of such modifying influences 
Moses and Solomon have given examfiles recorded by Josephus. 
Another instance is the advice given Iby Aristotle to Alexander as 
to the treatmentof certain perverse tribes : Change their atmosphere 
and thus change their morals ■• 390-394 

What deters students from the examination of this subject is fear 
of the imputation of magic. Doubtless astrology may be iturned to 
a bad account ; but so may the most useful of tools. Men do not 
dispense with weapons because malefactors use them, ^nor oease to 
go to law because some lawyers are dishonest. So, again, there is 
a strange force in certain words, uttered with full consciousness 
of their meaning, -which may co-operate with stellar forces. This 
too has been abused for purposes of magic and witchcraft, and dis- 
credit has been thrown on such agencies, which yet in wisc hands 
are useful. Like the stars, the human soul, whioh is nobler than 
they, emits forces from itself, which acting in harmnny with stellar 
forces may produce great results. The objection often made that, 
when the stars act on any object, they must act equaljy on other 
objects in the same horizon, is of no account : for no two objects are 
in the same horizon «...■.. 394-398 

Fascination, again, is a word with a bad sound. Yet important 
truth is contained in it. Influences radiate from certain persons, 
which may be good or bad, and which may be concentrated by 
a strong will and directed to a special object. Words used with this 
concentrated purpose may have great power. The exercise of 
miraculous power by the saints has been accompanied by words. 
We need knowledge of all these forces to resist the coming power 
of Antichrist. It is certain that the Tartar conquests have been 



cxxiv ANALYSIS OJ^ THE * OPUS MAJUS. 

VOL. I. PAGES 

largely assisied by confidence in their astrologers. Should they 
make cotninon cause with the Saracens, the results to Christendom 
may be disastrous. The children's crusade in the last century, and 
the fascination exercised by the Shepherd in our own time, are 
proofs of what hostile influences may do if not arrested promptly. 
What is needed is that all these influences, instead of being con- 
temptuously ignored, should be carefully studied, and used under the 
direction of the Head of the Church as a defence against the inroads 
ofAntichrist 398-408 



ANALYSIS OF THE ^OPUS MAJUS/ 



PART V. 

OPTIC. PART I. 

VOL. II. PAGKS 

In this section there are three parts. The first explains the general 
principles of vision. The second deals with direct vision. The 
third with reflected and refracted vision . . . .1-166 

In Part I there are twelve Distinctions. 

FlRST DlSTINCriON, DEALING WITH THE GENERAL CHARACrER 
OF OPTICAL SCIENCE, AND WITH THE ORGANS OF ViSION, 
PSYCHICAL AND CEREBRAL 1-12 

CHAPTER I. 
The superiority of vision to other senses has been pointed out by 
Aristotle and other authors. Vision reveals the difference of things. 
It supplies a knowledge of 'the heavenly bodies. It is the channel 
of experimental knowledge. Hearing can give faith, but not proof. 
Of the other senses we need not speak. Therefore the sense of 
vision becomes the object of a special science . . . .1-3 

CHAPTER II. 
The first thing is to determine the organs of the sensitive soul, 
which are to be found in the brain. Others have told us that the 
visual nerves issue from the brain ; but the account given is defective. 
The brain has two membranes— the Dura Mater, lining the cranium ; 
the Pia Mater, enfolding the brain. The brain has distinct chambers, 
or cells, each of which has its own function. In the anterior part of 
the first cell is sensus communis. This takes cognizance of, and 
distinguishes, the impressions brought by each special sense. But it 
is unable to retain these impressions, being loose and slippery. In 
the back part of the same cell there is therefore the organ of 
Imaginatiofi, which, being neither too moist or too dry, can retain and 
store np the material received by sensus communis. The combined 
opeiation of.these two orgaps is called Phantasi^ . • • ^-'^ 



cxxvi ANALYSIS OF THE ' OPUS MAJUS/ 
CHAPTER III. 

VOL. II. PAGES 

The attributes, or properties, of which sense takes cognizance may 
be reduced to twenty-nine heads. Nine of these are apprehended 
by sonie special sense ; as colour by sight, heat by touch, soimd by 
bearing. The other twenty may be called sensibilia communia, 
because apprehended by all, or by more than one, of the spectal senses. 
Distance, position, figure, number, rootion, rest, are among these . 5-7 

CHAPTER IV. 

But animals, though they have not intellect, have other faculties 
than those implied in the apprehension of these twenty-nine pro- 
perties. First there is the instinct prompting fiight from an animal 
of a dangerous spedes, or approach to one of its own, independently 
of experienoe. Each object in nature has its own constitution or 
complexion, and radiates corresponding impressions (species) which 
concur with those of like complexion, or disagree with those of unlike. 
They operate on special and on common sense, but are taken 
cognizance of by a higher faculty of the sensitive soul, which we may 
call the estimative sense, and may locate in the posterior cell of the 
brain. But as in the case of sensus communis, it does not retain its 
impressions, and needs another faculty acting as its storehouse, the 
memorative faculty. Midway between tbese two divisions or cells of 
the brain is the cell devoted to the cogitative faculty, the mistress 
faculty in brutes which have not true reason. By this faculty the 
spider weaves its web, the bird its nest. In man the rational soul, 
coming from without, uses tbis cogitative faculty as its chief in- 
gtrument 7-9 

CHAPTER V. 

That we do not find this view of the threefold division of the brain 
and of animal faculty in Aristotle is due to imperfect translation. 
It can be got from Avicenna, who has been better translated. And 
Avicenna is the greatest philosopher since Aristotle. In any case 
it will not do to confound the &culty which stores sensations with the 
faculty which stores judgements, under the common name of memory. 
It must further be stated that while placing these £sLcuIties in the 
brain, the substance of the brain is not itself sensitive, as Avicenna 
points out, respectfully correcting Aristotle on this point We must 
remember however that the sensitive soul has a twofold oi^gan— the 
brain and tbe heart The latter is the true seat of all life, as 
Aristotle maintains: the former is that which first receives im- 
pressions and in which the various operations of the senses are 
separately manifested 9-12 



PART V. cxxvii 

VOL. II. PAGES 

Second Distinction. 12-18 

GHAPTER L 

On the origin of the optic nerve& Clearly the function of vision 
cannot be understood without a knowledge of tfae structure of the eye. 
Most writers on Perspective have ig^ored this part of the subject, 
or contented themselves witfa a bare reference to work on medicine. 
I hope however to make the nuUter clear by reference to three 
authorities— Alhazen^ Constantine, and Avicenna. There are two 
cavities in the fore part of the brain called ventricles, one on the 
right, the other on the left. From. theae the optic nerves issue. 
They meet and cross ; the right nerve passing to the left eye, and 
conversely. In the hoUow of the eye the nerve spreads itself out 
in spherical fonn«. Each nerve consists of three coats, the innermost 
derived from the pia mater; outside this is one coming from the 
dura mater ; these two are wrapt in a third, coming from the lining 
oftheskull 12-15 

CHAPTER II. 

Thus the eye iiself consists of three coats ; containing three 
humours, and a structure like a spider s web (tela araneae). The inner- 
most is called by Avicenna and others the retina, and is supplied with 
veins, arteries, and slender nervous fibres ; the second, coming from the 
dura mater, is called the uvea ; it has an opening in front through 
which light passes. Behind, it is highly vascular : in front it is trans- 
parent and is called comea. The third and outermost coat is the 
sclerodc, which is firm and solid. It is sometimes called consolidativa ; 
it does not extend so far forward as to cover the cornea • . 15 16 

CHAPTER III. 

The uvea contains three humours, and also a web-like structure, 
arising from its anterior part. A crystalline or glacial substance fills 
the greater part of the cavity of the eye ; it consists of two parts. 
The hinder part, in contact with the terminal expansion of tfae ner^^e 
is like melted glass, thence called vitreous ; the anterior part, which 
has received various names, is like ice, hail, or crystal ; it is some- 
what whiter than the vitreous. Anterior to the web, occupying the 
space between it and the comea, is the third humour, somewhat 
like the white of ^%%. On the mode in which these parts receive 
nourishment there is some difference of opinion. Vision is dependent 
on the crystalline humour, thougfa not so essentially as on the optic 
nerve ••*•••••.•••# 17-18 



cxxviii ANALYSIS OF THE ' OPUS MAJUS/ 

VOL. II. PAGKS 

TUIRD DlSTINCTION. On the Sphericitv and Central : 
POINTS OF these Humours 18-25 

CHAPTER I. 

The eye approaches the most perfect of geometrical forms, the 
sphere. But between the various humours there are important ' 
differences of form. The crystalline is a portion of a sphere of 
different curvature from the vitreous. The centre of curvature of 
the vitreous is situated further forward on the axis of the eye ; that 
of the crystalline further backward. The comea has the same centre 
as the globe of the eye. The same may be said of the liquor albugineus. 
The centre of the uvea is anterior to that of the comea .' 18- 20 

CHAPTER II. 
It must be remembered that, in speaking of these bodies as spherical, 
we have only to deal with sections of spheres, relating to those parts 
of the eye concemed with the passage of light. In other parts these 
structures are not necessarily of spherical form .... 20-21 

CHAPTER III. 
The centre of the consolidativa is generally placed further back 
than that of the other parts. The truth is that it is not of strictly 
spherical form, neither is its inner surface concentric with the outer. 
Il is of irregular spheroid form, somewhat prolate on the forward 
surface. fiut the central points of all these ocular structures lie on 
one straight line, as the figure shows 21-25 

• FOURTH DlSTlNCTlON 26-30 

CHAPTER I. 

The comea doses the opening in the uvea, and prevents the 
escape of the aqueous. Being transparent it allows the passage 
of luminous impressions. It is strong enough to resist inroads of 
air and of dusty particles from without, being made up of four 
layers. Tbe aqueous is also transparent : its moisture prevents 
the crystaliine and iris from getting too dry. The uvea is usually 
black, so that feeble impressions of light and coiour may produce 
their fuU effect. It is however, from various causes, sometimes 
grey. The colour of the eye depends on this structure . . 26-27 

CHAPTER II. 

The anterior glacialis [lens] is connected very speciaily with the 
fttnction of vision^ It is moist, for luminous impressions wouid not 



PART V. cxxix 

VOL. II. PAGES 

aflect dry surfaces so readily ; it is of delicate stnictare, suited to 
subtle intluences of light. It is transparent, yet not too transparent, 
so that the passage of light may leave sufiicient traces to allow of the 
exerdse of judgement. Its surface forms part of a larger sphere than 
that of the vitreous, as already explained 27-28 

CHAPTER III. 

The vitreous is denser than the crystalline, so that re&action of 
the entering ray takes place towards the normaL Through it visual 
impressions are continued to the expanded fibres of the optic nerve. 
This nerve is the direct channel of communication with the brain. 
The consolidativa (sclerotic) is moist so as to adapt itself to the 
inward structures ; firm, so as to keep them la their places ; and 
white, so as to contribute to the beauty of the face . . . 28-29 

CHAPTER IV. 

The eyelids protect the eyes during sleep, and from iavasion of 
irritating particles ; thus the eyes have rest from the toil of receiving 
impressions. The lashes moderate the intensity of impressions. 
Creative goodness has supplied two eyes, in case of accident to one ; 
and to add beauty to the face. The eyes are spherical, so as to 
admit of easy and swift motion in all direcdons ; and also, because 
had their surface been plane, rays from the points of a large object 
would not have been normal to the surface. As it iis, perpendicular 
rays impinge upon their surface from nearly a fourth part of the 
horizon at once 29-30 

FlFTH DlSTINCTION 30-34 

CHAPTER I. 

We have now explained the instruments of vision. We pass to the 
function itself ; considering in the first place rectilinear vision. First, 
we find that impressions must emanate from the visible object, as 
Aristotle has shown to be the case in every kind of sensation. Vision 
is a virtus passiva ; but the passive must resemble the active, which 
in this case is the visible object Thus the species, or impression, is 
a likeness of the object. These species are thrown out as from 
a centre along every possible radius. Vision then takes place by the 
radiation of species, especially by those of light and colour. Colour 
has much to do with vision. A strong colour impression remains 
in the eye after the object has ceased to act on it. The species of 
light are even more easential than those of colour 

VOL. I. i 



cxxx ANALYSIS OF THE ' OPUS MAJUS! 

CHAPTER II. 

VOL. II. PAGE9 

Vision is not completed in the eye, but in the commissure of the 
optic nerves within the brain. Here the impressions coming from 
each eye coindde, so that the object is seen as single. If one of the 
eyes be forcibly misplaced, this coincidence does not take place, and 
the impression of duality is produced 82-33 

CHAPTER III. 
The terminal point of the visual process would seem to be the 
optic commissure : in the same way as the olfactory bulbs terminate 
the olfactory process. This in no way conflicts with what has been 
said as to the location of sensus commums. We are here speaking of 
special sensations. The function of vision then is partially carried 
on within the eye ; and is completed in the point of junction of the 
optic nerves 33-34 

SlXTH DlSTINCTION, CX)NTAINING EXPLANATIONS OF DlFFI- 
CULTIES IN THE FUNCTION OF VlSION 35-46 

CHAPTER I. 

A difficulty is suggested by the smallness of the pupil. Although 
cones of rays come from every part of the object to every part of the 
ocular surface, yet we need only consider for practical purposes one 
cone, made up of those rays which are normal to this surface. As 
to the oblique rays we shall see afterwards. Now it can easily be 
shown by geometry that from the base of a triangle, however large, 
any number of lines can be drawn to the vertex, which will all pass 
through any line subtending the base however short Matter is 
infinitely divisible : as many divisions can be made in a grain of - 
millet as in the diameter of the world 35-37 

CHAPTER II. 

But independently of the cone whose rays fall perpendicularly on 
the eye, there is an infinity of others whose rays fall obliquely. It 
would seem that confiision must result The explanation is that the 
perpendicular rays come with much greater force, and obscure 
the effect of the others, as the sun's light conceals the Hght of the 
stars. It has further to be observed that of these oblique rays many 
are made to converge by refraction with those which £dl per- 
pendicularly on the central part of the eye. There are thus various 
degrees in vision. The central rays and those which conveige with 
them are seen well : some rays result in imperfect vision ; some in 
noneatall 37-B9 



PART V, cxxxi 

CHAPTER III. 

VOL. II. PAGES 

A thiTd difficulty presents itself. The species from colours must 
mix throughout the medium ; black and white becoming grey, and 
so on; the mixture of species having the result as the mixture of 
their originals. The cone reaching the eye would thns present no 
distinctions of colour. The reply given by Aristotle, Averroes, and 
others is that these species have only a spiritual existence, and do not 
observe the laws of material forms. Any number of them therefore 
may meet in the same point without being mixed. But this view is 
profoundly erroneous. We shall find the true solution by recurring 
to what has been said before ; the preponderating force of the rays 
that fall vertically over all the rest Suppose the object to be 
black in the centre, white and red at the extremities. The black in 
their course will come into contact with white rays and red rays: 
but these latter will be oblique, and wiil therefore not affect the 
result. So with the rays from the white and the red parts of the 
object 39-42 

CHAPTER IV. 

Those who have spoken of species as spiritual, do not use that 
word as it is used of God or tbe Soul : they mean imperceptible. But 
such a use of the word is confusing. The species resembles tbat of 
wbich it is the image ; it is therefore materiaL It passes through 
a material medium ; is therefore material. It produces material 
results ; being related to that result as the incomplete to the com- 
plete, as the embryo to the fuUy formed animal. Species are indeed 
invisible, except it be by accident ; when an opaque body intercepts 
the ray of light or colour, we become sensible of it. Or again, weak- 
nes8 of sight may make us sensible of the passage of the ray, though 
we should not be so otherwise. The same principle applies to objects 
perceived by the other senses. It may be asked, How is it that three 
candles placed near a small opening appear as three on the other 
side? There is true mixture of the species in this case, for one 
illumination results. Stili if the eye be applied to the opening, the 
distinction of the principal rays proceeding from each will make 
itselffelt 43-46 

SBVENTH DlSTINCTlON . 47-53 

CHAPTER I. 

* Importance of the difierence in density between crystalline [lens] 
and vitreout. If the vitreous were of the same density as the lens, 
the rays passing from the latter to the former would foUow their 

i 2 



cxxxii ANALYSIS OF THE * OPUS MAJUS: 

VOL.n. PAGES 

straight path. In this case a ray falling on the right side of the lens 
would pass backwards to the left of the eye, and conversely. Con- 
fusion as to right and left would thus result. But, the vitreous being 
denser, the rays leaving the lens are refracted ; and as the diagram 
shows, they converge in a way which avoids this confusion . . 47-49 

CHAPTER II. 
The action of the eye on the object seen. Like every other object, 
the eye radiates species. But are these radiations, or those of them 
which touch the object, necessary to vision ? AristotIe's remarks in 
his treatise on Generation seem to point to this. Ptolemy and 
subsequent optical writers have asserted it. Plato maintained that 
sensation was whoUy active ; the Stoics that it was wholly passive. 
Aristotle takes a medium course. Vision is in fact not merely 
passive, but active 49-50 

CHAPTER III. 
Nor do Alhazen, Avicenna, and Averroes contest this view. They 
only protest against the notion that the eye emits some material 
substance to the thing seen. A passage in Aristotle {De Anima/u, 
12) has been understood as though he looked on sensation as wholly 
passive. But it was only by way of protest against the Platonists, who 
went too far in the opposite direction 50-52 

CHAPTER IV. 
As all objects in nature complete their action by emitting their own 
special forces, so does the eye generate rays from itself. These meet 
the rays proceeding from the object to the eye, and facilitate the 
passage of these latter. As they are of different nature no confusion 
arises from their meeting 52-53 

ElGHTH DlSTINCTION. FOUR OF THE CONDITIONS REQUIRED 
FOR VlSION 54-61 

CHAPTER I. 
The first condition is Light. Without light, colour either (a) does 
not exist, or [b) sends out no emanations, or {c) what emanations it 
produces do not affect vision. The third of these explanations is the 
true one. The second condition is, Distance of the object. An object 
placed in immediate contact with the organ of sense is not perceived : 
for the organ acts by emitting force from itself into the medium. 
This is the case even with the senses of touch and taste. The 
medium for these is the flesh and skin surrounding the sense 
organs 54-56 



PART V, cxxxiii 

CHAPTER II. 

VOL. II. PAGES 

The third condition is the Position of the object in respect of the 
eye, They must be connected by straight lines either direct, re- 
fracted, or reflected. Why is this the case with vision, and not so in 
the case of hearing, or of the sensation of heat ? Aristode here fails 
us. Thedifficulty is obvious. A man can hear his own voice : why 
cannot he see his own face ? It would seem that sound generates 
something more than species of sound : it must generate sound itself. 
The trembling of the air following on that trembling of the object 
struck which constitutes sound, is propagated in all directions, and 
is therefore perceived as sound everywhere. In the same way an 
odorous body not merdy sends out species, but subtle material 
particles, which being diffused through the air themselves emanate 
in every direction. It has been already explained that there are 
certain qualities capable of completing their species, by generating 
fresh sources of radiation. Fire is one of those .... 56-58 

CHAPTER III. 

The fourth condition of vision is that the object be of suitable 
Magnitude. Each point of the object must be represented on the 
surface of the lens. And although that sur&ce, like all others, is 
iniinitely divisible, yet, for purposes of sensation, the division must 
not go so £ur that the points become undistinguishable. Again, the 
object must not be too large. What are the limits ? If the extreme 
angle of vision be a right angle, an eye placed at the earth's centre 
would see one fourth part of the heavens; at the earth's surface 
something less, as geometry shows. The view that the limit of the 
angle of vision must be a right angle rests on no sound basis, either 
of tbeory or experiment. Examination of the structure of the eye 
fumishes geometrical proof that it is less than a right angle. And 
experiment makes this certain 58-61 

NlNTH DlSTINCnON. OXHER CONDITIONS OF VlSION . . 62-74 

CHAPTER I. 

The fifth condition of vision is that the Density of the object 
shall exceed that of the air and of the heaven. This is why we 
see water, glass, and other transparent bodies. Air we can only see 
when accumulated in great masses, which produces the same result 
as density. So the most transparent water becomes opaque if the 
depth be very great, shadows being cast by each particle of water 
on that which succeeds to it. Further, we have to note that the 



cxxxiv ANALYSIS OF THE ' OPUS MAJUS: 

VOL.II. PAGES 

power of the eye to send out radiations, which we have seen to 
be an essential factor in vision, is limited. And as such limitation 
of penetrating power implies visibility, we have in extreme distance 
a reason why extremely rare bodies become visible. The blue colour 
of the sky is to be explained as in the case of deep water. Blue is 
the colour which most nearly approaches blackness ; it results here 
from the shadows thrown by each partide of air on succeeding 
particles. If the heavenly spheres were opaque, it might be supposed 
that they would be visible objects. But theological reasoning shows 
that they are not opaque. Beyond the eight stellar spheres is the 
sphere of water, and beyond that again the tenth. It may be asked 
how is it that we see a ray of light passing through a window, though 
in this case the air being warmed by the sun is rarer than the air 
surrounding it ? The reply is that what we see is not the luminous 
ray but the boundaries of the denser air which it penetrates. As to 
the heavenly spheres, it has been already shown that they are 
themselves transparent, the star placed in each of them being 
opaque 62-66 

CHAPTER II. 

The sixth condition of vision is Rarity of the Medium. It is 
objected that flame is rarer than air, and yet that a flame placed 
between the object and the eye impedes vision. But it is a 
mistake to suppose that flame is rarer ; and Alhazen, who has been 
quoted as saying this, is misinterpreted. Whether a lynx sees 
through a wall or not, the human eye which we are here considering 
certainly does not On the other hand, we are not to suppose 
a vacuum between heaven and earth. Radiation of species would 
be impossible in that case. A vacuum is a mere mathematical 
abstraction 66-67 

CHAPTER III. 
The seventh condition is Time. Time, as Aristotle shows, is needed 
for an act of memory : much more for an act of sensation. It has 
becn maintained that radiations from the object and the eye take 
place in an indivisible instant of time. For if not, then the particles 
of time, however small, would form a perceptible aggregate while the 
radiation passes from the east of the heavens to the west. This 
view is held by all but Alhazen, and by him is contested on in- 
sufficient grounds. Some however of his arguments against it are 
sound, resting as they do on Aristotle^s doctrine that finite energy 
requires time for its operation, the time being inversely as the 
energy. Suppose the energy inflnite, then, and then only, does 
the time become zero. The notion that th^ ray is spiritual not 



PART V: cxxxv 

VOL. II. PAGES 

materia], and therefore not amenable to physical laws, has been 
already disposed of. It is material, and as such cannot be in several 
places at the same time 68-71 

CHAPTER IV. 

It may be fiirther observed that the time occupied by a luminoas 
radiation may be so small as to be imperceptible to our senses even 
when the distance traversed is very great. Aristotle^s supposed 
denial of it was a denial of the view of Empedocles that a corporeal 
body was transmitted across space. But the luminous radiation is 
not a body, but a form axitinuaHy renewing itself out of the particles 
of the medium, as it travels. It is true, as Aristotle says, that tbere 
is a difference between the transmission of light and that of sound 
and other sensory impressions. With sound there are three distinct 
displacements of material partides, viz. motion of the body stnick, 
tremor of the air, and rarefaction of the air. Nothing of this kind 
takes i^ce with light, for though light makes heat and rarefies the 
air, yet it is transmitted throi^h celestial spaces where rarefaction 
and heat-production is impossible. In the tiansmission of odours, 
again, there are special differences. But all need time : though not 
the same time. We see the stroke of a distant hammer before we 
hear it Lightning reaches us before thunder. 

The eighth condition is a healthy state of the eye. A final con- 
dition, relating to the axis of vision, will be spoken of afterwards 
(p.97) 71-74 

Tenth Distinction 74-82 

CHAPTER I. 
We may now inquire with greater precision of what matters vision 
takes cognizance, what degree of certainty it brings, and to what 
errors (limiting ourselves to direct vision) it is exposed. Knowledge 
is either given to us directly and immediately by Sense, or indirectly 
and fier accidim, Supposing the eight conditions described to be 
ppesent in just degree, the eye will perceive the twenty-two qualities 
previously noted, with or without the help of the other special senses, 
and of Sensus Communis and Imaginatio (pp. 4-5). By qualities 
indirectly sensible I mean those which oome under our cognizance 
through sensation, but which are appreciated by other faculties, as 
judgement ; as when a lamb seeing an object of the form and colour 
of a wolf, knows it to be an enemy. When I see a mauy I see an 
animated object and a substanoe ; thus in an indirect way substance 
6iay be spoken of as sensible* Again, the sensations peculiar to one 



cxxxvi ANALYSIS OF THE * OPUS MAJUS: 

VOL,II. PAGKS 

of our senses are indirectly appreciated by another, as when we see 
iron to be hot, or ground to be wet For cold, heat, moisture and 
dryness cannot be directly appreciated by the eye • . • 74^76 

CHAPTER II, 

The question arises, Do all sensible things of which the eye takes 
cognizance propagate rays to the eye, or light and colour only ? The 
latter is the true view. These other things are magnitudes or 
properties of magnitudes, and belong to matter, which is passive, not 
active. The air which is the medium of sound is itself soundless, and 
the medium of colour, colourless. They are called sensible, not 
because they emit species to the sense, but because the sense 
appreciates them. AU that is really necessary for vision are the rays 
of light and colour, combined with the ray directed to the object from 
thecye 76-79 

CHAPTER III. 

Knowledge comes to us in three ways : (i) by sensation pure and 
simple, as when a colour strikes the eye without remembrance of any 
previous colour ; (2) by similitude of the present sensation with 
a past sensation remembered ; (3) by a ratiocinative process, as 
when we judge an object to be transparent because we are able to 
see an opaque body behind it But, although the process by which 
our perception takes place is one of reasonmg, it takes place so 
instantaneously that we are not aware that we reason. We are 
logicians instinctively, without having names for the various steps 
which the mind takes. These three modes of knowledge have been 
inappropriately named, Sensation, Science, and Syllogism . . 79- 82 



OPTIC, PART II. 
Special consideration of Direct Vision • . . 83-129 

FlRST DlSTINCTION. ON VISION AS DETERMINBD BY THE 

Structure of the Eye 83-91 

CHAPTER I. 

Those whose cycs are deep-set see furthcr than those whose eycs 
are promincnt. First, bccausc the eye is nearcr to the brain. 
Secondly, because it is better preserved from cxtemal injury. 
Thirdly, because the visual force bcing coropressed within a 
narrower channel issues with greatcr eneigy and directncss. Wc 
often proloDg this cbannel by holding the hollow of thc hand 



PART V. cxxxvii 

VOL. II. PAGES 

before the eye when we wish to see very distinctly. Eye-lashes help 
in the same direction. In fishes which have none, the visual force is 
dispersed. So too it is that ftom the depth of a well we are able to 
see the stars. The amount of the aqueous humour in front of the 
lens would also affect vision. Those who have little see further than 
others, for deep water, though transparent, yet is a bar to the trans- 
mission of light. It may be observed that old people hold objects 
that they wish to examine further from the eye. The reason is that 
their eyes abound in moisture : and the object to be clearly visible 
must be placed beyond the range of that moisture . . . 83-86 

CHAPTER II. 
Distinctness of vision does not always accompany length of vision. 
It depends on the sufficient size of the lens, on the purity of all the 
humours of the eye, and on the absence of that degeneration of the 
comea and the capsule of the lens wbich comes with age, and which 
involves ihe casting of shadows. Why is it that some eyes see better 
in the dark than others ? Absence of moisture and extreme trans- 
parency in the ocular structures conduce to this result ; such eyes 
are overpowered with light in the daytime, and see badly. P^urther, 
the eye has a certain amount of independent luminosity ; greater in 
some men and animals than in others 86-88 

CHAPTER III. 
Double vision results from disturbances in ocular structures. In 
the normal condition of the eyes, the object seen appears single. 
If the eyes are congenitally or forcibly displaced, this unity of the 
object is lost. Extreme heat or cold may produce this result; or 
anger, infirmity, or drink. Duplicity of vision may depend either 
on displacement of the vitreous humour, or of the nervous spirit pro- 
ceeding from the brain to the eye, or on dilatation or contraction 
of the uvea. In some cases there may be an exudation covering a 
portion of the lens. Another cause of duplicity has been suggested. 
The radiations issuing from tbe eye may be so feeble as to be stopped 
not merely by the object of vision, but by some one of the radiations 
from this object. It is stated also that in some cases the eye has 
had two pupils, though I have not myself seen this . . . 88-91 

Second Distinction. On Radiations from the Object 

AND FROM THE EYE, AS AFFECTING DIRECT ViSION . . 92-99 

CHAPTER I. 
How is it that we see a doud at a distance, whereas wben dose to 
it, or immersed in it, we do not ? The answer is that the radiations 
VOL. I. k 



cxxxviii ANALYSIS OF THE ' OPUS MAJUS.' 

VOL. II. PAGES 

from thc eye are strong enough to penetrate it when near ; not so 
when distant. We must conceive the pencil of rays from the object 
and that from the eye as having a common axis drawn through the 
various ocular centres; this central line being specially potent in 
vision. The point at which it strikes the object is seen with 
cleamess ; adjacent points also, in proportion ' to their proximity. 
The axis of the eye is directed successively to each point in the 
object. The eyes act in concert, their axis being directed to the same 
point 92-94 

CHAPTER II. 

When one of the eyes is pushed by the finger from its proper 
position, the angle of vision ceases to be the same for both of them, 
and the object appears double. So too when the eyes are fixed on a 
given pointy an object placed between that point and the eye, or 
beyond that point, will appear double. It is easy to demonstrate this 
byexperiment 94-95 

CHAPTER III. 

Further experiments on double vision may be made. If the finger 
be held between tbe eye and a candle, and the eyes be fixed on the 
candle, the finger will appear double. If the right eye be closed, the 
left image will disappear. If however the light be very distant, 
the result is different. The right image vanishes on closing the right 
eye 96-97 

CHAPTER IV. 

Again, the axes of each eye may make such an angle with the 
common axis of vision as to produce a doubleimage. Or thedirection 
of any point in the object of vision may make such an angle with the 
axes of the eyes that the point is seen double .... 97-99 

Third Distinction' 9^129 

CHAPTER I. 

Lct us consider further the three modes of pcrception, through sense, 
through recoUcctiony and through argument, in reference to the eight 
conditions of vision. Light and colour are appreciated through sense 
only : and this without error, so long as the right conditions of vision 
are fulfilled without excess or defect. Starlight is not seen by day 
because of excess of solar light. Diminish the latter, as by descending 
to the bottom of a welly and the stars are seen. The Milky Way, 



PART V. cxxxix 

VOL. II. PAGES 

consisting of a multitude of small stars clustered, pioduces the 
erroneous impression of a continuous light; this is due only to 
distance. This luminous impression is caused by the passage of 
rays from these small stars through the sphere of fire ; the medium 
in the stellar spaces would be too rare, that of the sphere of air too 
dense. We have also to take into account the refraction of rays in 
the sphere of fire ; but of this afterwards. The light of dawn raises 
a question. Why do we not see it earlier ? Why, since outside the 
earth'% shadow the whole sky is illumined, does the sky appear dark 
to us? The reply is, first, that the spheres of heaven are very 
distant ; also that the heaven, apart from the dense bodies contained 
in it, is too rare to have fixed light ; light passes through it without 
affecting the eye. When the sun's rays touch that portion of air 
which is comparatively near to us, this iUuminated air becomes per- 
ceptible. It may happen that a luminous body of small magnitu^e 
appears far lai^ger than it is on account of rapid motion. Sparks 
from a fire produce this effect. Shooting stars are probably bodies 
of small magnitude. Colour, like light, is apprehended by pure sense ; 
and correct apprehension of it depends on the conditions before men- 
tioned. Extreme transparency of the object, great intensity of the 
colour, too great remoteness of it, rapid succession of different 
coloursy will inter£ere with accurate perception .... 99-104 

CHAPTER II. 
Of Perception through knowledge (recollection). Under this head 
are to be classed distinctions of characters, wbether general or special, 
in visible things. The moon's light outside the earth's shadow is 
dear and white, in the upper part of the shadow red, in the lower 
part is invisible. These differences, though perceived by sight, become 
known to us only after repeated observation. The explanation is not 
easy. The moon*s light, like that of other stars, comes from tbesun. 
When the moon is in conjunction, the hindrance to illumination of 
the part of the moon tumed to us is the moon itself ; the solar rays 
diverge widely on either side, and do not reach us, even secondarily, 
by dispersion. But when the moon is in the earth*s shadow, the earth 
being distant from the moon, the moon is near thevertex of the cone, 
and accidental solar rays entering within it produce the reddish light 
seen in a lunar eclipse. The degree of this light will vary with the 
distance of the moon from the earth at the time of eclipse, which may 
be greater or less. Another problem, raising a similar difficulty, 
occurs with colour. If we look through a very thin piece of parti- 
coloured cloth at isin object of given colour, we may see that colour if 
tbe apertures in the web are lai^e enough; if otherwise, we see 
a mixed colour. The quality of the medium will modify the result. 

k2 



cxl ANALYSIS OF THE * OPUS MAJUS: 

VOL. 11. PAGKS 

The rays, in this case, coming from the threads of the web are so 
nearly coincident with the rays coming from the object, as to be con- 
fused with them 104 106 

CHAPTER III. 
Of Perception through reasoning. Many examples can be given 
of this. The most striking is our perception of distance. An object 
may be so distant, as to subtend so small an angle in the eye that 
vision ceases. Short of that limit, the degree of distance is deter- 
mined by a continuous series of objects between the object and the 
eye. In a flat country we have no means of judging the height of 
the clouds, which we can do when we see them on the sides or 
summits of mountains. [Clouds would appear to be of no great 
height, though, as we know from the fact of twilight, exhalations 
other than clouds may rise fifty-one miles. Such exhalations are 
not aqueous : being dry they retain the sun's heat better, and thus 
rise higher.] For judging, then, of distance, we must have an inter- 
mediate series of objects, each of which shall be appreciable by the 
eye with sufficient accuracy. These limits are soon exceeded. 
A line of trees appears continuous, though there may be a great 
interval between each of them. So planets seem to be in the same 
surface as fixed stars, though the difference of remoteness is 
immense. So an equilateral figure of many sides becomes at 
a distance undistinguishable from a circle. A circle may be taken 
for a straight line, a sphere for a plane figure. When a circie is held 
sideways before the eye, the part nearer to the eye will be recognized 
as nearer if the distance is moderate : if it is very far ofT, the difference 
of distances in the points bears so small a proportion to the whole 
as not to be recognized. Thus it is that, when the moon is in her 
first or third quarter, the circular line defining the light part from the 
dark appears as a straight line. So too the sun and moon seem to 
us flat, though they are spherical 106-108 

CHAPTER IV. 
AII this is exempHfied in the study of the Moon*s Phases. The 
base of the cone of solar light occupying the moon's surface appears 
to us twice in the month as a straight line ; otherwise as curved : 
a fact unexplained in the Latin translations of Aristotle and Averroes. 
Here we have to leave the region of sense, and penetrate to the 
real facts, which, but for the remoteness of the sun and moon, we 
should be able to see. The boundary of rays proceeding from one 
eye to the moon is a great cirde of that body ; that of rays proceed- 
ing from the sun to the moon is also a great circle, or nearly so. At 
conjunction and at full moon these circles coincide, the lunar surface 



PART V. cxH- 

VOl.II. PAGES 

presented to the earth being wholly conceakd or whoUy illuminated. 
At other times the illuminated surface is represented by the space 
]eft between the intersections of two great circles, the points of 
intersection being at the extremity of a lunar diameter. Regarding 
these points as the lunar poles, the inner boundary of the illuminated 
part may be regarded as a meridian circle. A circle drawn through 
the lunar poles so as to divide the lunar surface visible to us into 
two equal parts may be called the lunar colure. The inner boundary 
of the luminous portion becomes identical with the colure on the 
seventh and twenty-first day, and appears to us as a straight line. 
Before the fourteenth day this circle presents its convex side to the 
sun, after that day its concave side. In the latter half of the month 
the phases are seen reversed till complete occultation retums. 

So too by a reasoning process we become convinced that though 
the heaven appears to us as a plane surface, it must in reality be 
spherical, or at least polyhedral, so as to be undistinguishable from 
a sphere. Were it plane, the stars would all disappear below the 
horizon or rise above it at the same moment .... 108-114 

CHAPTER V. 
As distance is appreciated only through a reasoning process, so it 
is with magnitude. The mere magnitude of the angle subtended by 
the object does not suffice, for objects of the same magnitude at 
different distances appear of different magnitude, and conversely. 
As in the case of distance, there must be intermediate objects familiar 
to the eye with which raental comparison can be made. Extreme 
distance often renders such a comparison impossible . . 114-116 

CHAPTER VI. 
The eye looking at a sphere sees somewhat less than the half of 
it, as the third book of the EUments shows. Heavenly bodies look 
larger at rising and setting than when at the meridian. Why is this ? 
When looking either to east or west, the sky seems a plane, or nearly 
plane, surface stretched overhead. What is over the head seems 
neaier to us, and subtending the same angle, is judged smaller. 
Furthcr, owing to the interposition of terrestrial objects between our- 
selves and the rising or setting star, we are better able to appreciate 
its distance, and thus are led to imagine it larger. Our perception 
of motion and rest depends also on a reasoning process. Motion is 
apprehended by a change in the position of a body relatively to 
another, the change involving a lapse of time. Rest is the absence 
of such a change. Hence illusions arise. When clouds are driven 
across the moon, the moon seems to be moving through them. The 
clouds must be numerous and almost continuous for this effect to be 



cxlii ANALYSIS OF THE ' OPUS MAJUS: 

VOL.II. PAGRS 

produced. Again, while we axe walking at night in any direction, 
a star to the right of us will seem to move with us, since it holds 
very nearly the same position relatively to us at tbe end of our 
passage as at the beginning: the star being far off, the difference 
made by our change of place is imperceptible. When the sun is 
on the meridiany a long line of men extending from east to west will 
all see him directly in front and the shadows of their bodies will 
appear parallel ; the divergence of the shadows is too small to be 
perceptible. The motion of the planets is imperceptible by direct 
inspection. Rapid motion in a cirde, followed by rest, gives the 
sensation of movement in surrounding objects. In this case when 
the man stands still, the humours of the eye still continue in motion. 
In a moving ship, trees and houses on the bank seem to move, 
especially if distant : if the eyes converge on a near object it will seem 
stationary 116-119 

CHAPTER VII. 

One of the most difiicult problems is that of the scintillation of the 
fixed stars. Aristotle remarks their contrast in this respect with the 
planets, and attributes it to their greater distance ; the eye, being 
more strained, is tremulous. Scintillation is different from the tremor 
sometimes seen in the sun and other planets at rising and setting. 
If distance were the sole explanation, we should expect Satum to 
scintillate, which it does not. Further, it is only the lazger of the 
fixed stars that do so. Therefore strength of light must be a condi- 
tion. And yet, since the sun at noon does not scintillatey the light 
must not be too strong. One of the causes would seem to be the 
internal strain of the eye at very distant objects. The planetary 
bodies are easily perceived to be near, and with them there is no 
strain. Moreover, the fact of extreme distance of itself weakens the 
visual rays. It may be objected that the strain is greater in the case 
of small stars than of large : but here the condition of sufficiently 
strong light is wanting. Again, it is objected that if ocular strain 
be one of the factors, this depends upon each observer's choice and 
will. But this is not so. It is one of those actions which have 
become involuntary through habit. But how is this difference 
of distance between the planets and the stars to be known ? Its 
quantity doubtless is not known. But the fact that there is a 
difference is a matter of sensation. Has the density, or has the 
motion of the medium, anything to do with scintillation ? Perhaps 
both contribute, as Averroes has suggested ; and perhaps also at 
these immense distances the visual power is exhausted, and acting 
only intermittently, produces the tremulous impression. By motion 
of the medium we are to understand herei not violent motions of the 



PART V. cxliii 

VOL.II. PAGES 

lower air like wind, bnt subtle motions caused by tbe revolutions of 
the heavens and of tbe exbalations whicb pervade tbem. A com- 
bination of tbe foregoing causes inay snfficiently explain this 
coraplicated probkm 120-126 

CHAPTER VIII. 
We may now snm up the results of our study of direct vision. We 
have spoken of vision as operating by sensation, by recollection, and 
by a syilogistic process. If tbese two last are to be interpreted as in 
the schools, tbey would imply the intervention of Reason. But it is 
evident that brutes bave the power of recognizing and distinguishing 
botb universals and particulars. A dqg recognizes a particular man, 
and also recognizes men in general from dogs, trees or other objects. 
Tberefore this facnlty must be a function of sensitive life, and cannot 
imply reason in the strict sense of that word. Further, animals pass 
through a train of mental processes analogous to syllogistic reasoning, 
though they cannot put it into a logical figure. Tbey have a store- 
house of mental impressions. They can generalize, and tbey can 
draw conclusions ; tbough they are not conscious of doing so, and 
cannot give an account of what is passing witbin them . 126-129 



OPTIC. PART III. 
FlRST DlSTINCTION : On Rbflected Vision . . . 180-146 

CHAPTER I. 
It is unnecessary to repeat what has been already said of tbe 
structure of the eye and the functions of sensation. Bodies that 
impede the passage of visual radiations may be either wholly 
opaque, as a stone wall ; or partially opaque, as water, glass, 
crystal. Opaque bodies do not destroy the radiation : tbey merely 
alter its patb. An opaque body may be rough or smootb. When 
the surface is rough, the parts being unsymmetrical scatter the 
radiations irregularly, and there is no image. With smooth surfaces 
the parts all act alike, and the radiation comes back to tbe eye 
uninjured, though feebler tban in direct vision. Proof is subjoined 
of tbe equality of the angles of incidence and reflexion, and this proof 
will hold, whether the surface be plane or spherical : for tb^ ray may 
be regarded as falling on the tangent plane .... 190-132 

CHAPTER II. 
Tbe mirror contains notbing. What is seen is the real object, 
only the radiation from it has foUowed an angular course. The eye 



cxliv ANALYSIS OF THE ' OPUS MAJUS: 

VOL. II. PAGES 

must be situated at the extremity of that course, whether it has been 
straight or angular, in order to receive the impression. It follows 
that the radiation produces no durable efTect on the reflecting 
surface. From this again it follows that the moon and the stars 
shine with their own light, not with light reflected from the sun : 
otherwise we should see the sun's image reflected in them. Neither, 
again, is a comet the reflexion of solar light from the surface of 
a star. The case of the rainbow will be considered afterwards. The 
position in which we judge the reflected object to be is, in plane 
mirrors, at the intersection behind the mirror of the prolongation of 
the reflected ray with that of the perpendicular let fall on the mirror 
from the object But in mirrors other than plane the apparent 
position varies very greatly 182-134 

CHAPTER III. 
There are seven kinds of mirrors, spherical, conical, cylindrical, 
or plane. Of the first three classes each may be cither convex or 
concave. Geometrical proof is given that in plane mirrors the image 
and the object appear equidistant from the plane of the mirror on 
opposite sides. Nothing reaUy takes place either in the mirror or 
behind it. The effect produced is a mental impression caused by « 
the peculiar path taken by the radiation from the object. In spheri- 
cal convex mirrors, the intersection of the visual ray with a line 
drawn from the object to the centre of the sphere fixes the apparent 
I>osition of the object This intersection may be beyond the mirror, 
in the mirror, or on the same side as the object. Usually the image 
appears less than the reality, because the rays come from a smaller 
area than in the case of the plane mirror : in the spherical most of 
them are dispersed. The image is erect but distorted: the outer 
rays of the cone touching points more distant from the eye than the 
median rays. Only when the image of a right line crosses the centre 
of the sphere is that image rectilinear. Moreover, in convex mirrors 
the image is nearer to the mirror than the object isj because the inter- 
section of the visual ray with the perpendicular occurs sooner in 
spherical than in plane mirrors. In cylindrical mirrors the errors 
are even greater than in spherical, except in the one case where 
a line in the object is equidistant from the axis of the cylinder. 
Only if this line has any breadth, its transverse magnitude will be 
distorted. In convex conical mirrors the same errors occur as in 
convex spherical 134-137 

CHAPTER IV. 
The greatest illusions are those that occur in concave mirrors, both 
as to the size of the image» and the number of its repetitions ; some 



PART V. cxlv 

VOL. II. PAGBS 

of these being inverted^ some erect. The two diagrams accompany- 
ing this chapter illustrate these effects 137-141 

CHAPTER V. 
Many observations of natural objects show the dependence of 
colour on the angle at which the light falis, as for instance the 
plumage of the peacock*s tail or the pigeon's neck, and also the rain- 
bow, as we shall see in dealing with experimental science. Drunken 
men or those in weak health see their own image projected in front 
of them. Seneca explains this by a supposed feebleness of the 
radiations proceeding from their eyes, which instead of penetrating 
the air are reflected back as from a mirror to their bodies ; and the 
eye thus perceives the body to which it belongs. It may be supposed 
that the air round persons in this condition is specially charged with 
morbid vapours, capable of reflecting the radiation. On this hypo- 
thesis it is objected that the strongest radiations from sound eyes 
would be ultimately reflected from the clouds. But their distance 
and their uneven snr^ce prevent such reflexion. In the case of 
drunken or weak persons we need not accept Seneca's view of 
emanations from the eye reflected from vapour. We may suppose 
tl^e emanations from the object, i. e. from the person, to be weak and 
to be easily stopped, and so to become an object of direct vision. Thc 
rays seen projected from a candle are due to the light falling in 
certain directions on the eyelashes, which being polished surfaces, 
act as minute mirrors. The scintillation from a metallic surfece in 
an elevated position, as from a cross on a church tower, is due to the 
motion of the sun or moon whose light is reflected from it . 141-144 

CHAPTER VI. 
If a mirror be placed in a vessel of water and the image of the sun 
reflected from it, a second image will appear beside the first, which 
was held to be that of a star. If it were, the sun's light would hide 
it Moreover, the same effect is produced by the moon or by 
a candle. There are in fact here two mirrors, the surface of the 
water and that of the mirror. That from the mirror is more perfect, 
the other being weakened by the loss of some of the rays through 
refraction. Fracture of a mirror does not necessarily result in 
multiplication of images, unless the pieces are removed from each 
other 144-146 

Second DiSTiNCTiON : On Refraction . • • . 146-159 

CHAPTER I. 
We now come to the question of refraction. Rays passing from 
a point in the object towards the eye are refracted at the comea, 



cxlvi ANALYSIS OF THE ' OPUS MAJUS: 

VOL.II. PAGES 

which is denser than the air, towards the normal ; with the exception ^ 

of such rays as fall vertically on the comea. The same point may ( 

emit a vertical ray and also an infinite number of oblique rays, these 
latter co-operating in the act of vision 146-148 

CHAPTER II. 
The interseetion of the perpendicular directed from a point in the 
object with the visual ray determines the apparent position of that 
point. If the eye be in the rarer medium and the object be in the 
denser the point appears nearer than it really is ; and conversely 148-149 

CHAPTER III. 
The case is complicated if the surface separating the two media 
be not plane but spherical. Here we have eight distinct cases. 
I. When the curved refracting surface is concave to the eye. l. The 
eye being in the rarer medtum, {a) the eye is between the centre of 
curvature and the object, (b) the centre of curvature is between the i 

eye and the object 2% The eye being ki the denser medium, cases 
(a) and {b) as before. II. When the curved refracting surface is y 

convex to the eye. i. The eye being in the rarer medium, (a) the 
object may be between the centre of curvature and the eye, (b) the 
centre between the eye and the object. 2. The eye being in the ' 

denser medium, cases {a) and. {b) as before .... 150-153 

CHAPTER IV. 
Examples of the foregoing. Tbe snbmerged part of an oar 
illustrates case i of ch, 2. If the eye were under water the upper 
part would illustrate case 2. If an object be placed in a basin, and the 
observer step backwards till it becomes invtsible, the object will again 
become visible by pouring water into the basin. This again illustrates 
case 1. The sun and moon when near the horizon» where vapours 
abound, seem larger than ustfaL The vapours form a lens with the con- 
cavity towards the eye : the eye being between the centre of curvature ' 

and the object. The object therefore seems larger and nearer. Why i 

then do the sun and moon not appear larger <when they are high up 
and the sky is cloudy ? Because in this case there is no refraction, 
or but little. So there is no apparent increase of size when, the 
horizon being free from vapour, there is no refraction. The angle 
under which the celestial object is seen is of more importance in 
forming our judgement than the apparent distance, since the absence 
of intervening objects makes judgement of distance difficult. A crystal 
lens if consisting of a small portion of a sphere, with the convexity 
tumed to the eye, will magnify small objects placed beneatb it, in 



PART V. cxlvii 

VOL. II. PAGES 

accordance with the fifth rule. If it be the half of a sphere or more 
than the half, then the centre of the sphere will be between the eye 
and the object and the magnifying effect will be less. A candle 
however held at a moderate distance will appear larger than if 
placed nearer, because the refracted rays from the extremity of the 
object are taken for direct rays. Moreover, rays from the nearer 
position are apt to dazzle a weak vision and thus are neutralized. 
From a somewhat more distant position they are better appreciated. 
These are a few illustrations of the effects of refraction. They are 
not intended as an exhaustive treatment of the subject. . . 153-159 

Third and last Distinction 159-166 

CHAPTER I. 

All these scientific truths have a spiritual signification. The prayer, 
Guard us as the pupil of thine eye, cannot be understood without 
knowledge of the structure of the eye and the pupiL £ach of the 
structures by which the pupil is defended has an allegorical 
meaning 159-161 

CHAPTER 11. 

As in vision we should neither be too far from the object nor too 
near, so for spiritual vision we should neither be too far from God, 
nor too presumptuously near. Vision is by sense, by memory, 
and by reasoning ; this may be paralleled in spiritual vision. Vision 
is direct, refracted, or reflectcd: spiritually the first is divine, the 
second angelic, the third human. Or, again, the first is the perfcct 
vision after the resurrection ; the second,ibefore resurrection and after 
death ; the third, the imperfect vision of life on earth . . 161-163 

CHAPTER in. 

On the practical application of this science there is much to be 
said. By reflexion we can multiply the images of objects at will, 
as by natural mirrors formed by vapours in the sky the image of 
the sun and moon are multiplied. Mirrors may be erected in 
elevated positions which may reveal the details of an enemy's camp, 
as is said to have been done by Caesar from the coast of Gaul when 
about to invade Britain 164-165 

CHAPTER IV. 

By refiraction even greater wonders may be wrought ; small things 
may be made to seem great, distant things near . . . 165-166 



cxlvui ANALYSIS OF THE ' OPVS MAJUS.' 



PART VI. 

VOL. II. PAGES 

EXPERIMENTAL SCIENCE 167-222 

CHAPTER I. 

Having laid down tbe general principles of wisdom so far as they 
are found in language, in mathematics, and in optics, I pass to thc 
subject of experimental science. There are two modes of acquiring 
knowledge — reasoning and experience. Reasoning guides us to 
a sound conclusion, but does not remove doubt from the mind until 
confirmed by experience. A man who has never seen fire may read 
the proofs that fire bums, but will not be satisfied of it till he has been 
bumt. Even in geometry the demonstration of the first proposition 
of Euclid fails to carry conviction till the figure has been inspected. 
When Aristotle speaks of knowledge of the cause as a higher kind 
of knowledge than that gained by experience, he is speaking of mere 
empiric knowledge of a fact ; I am speaking of experimental know- 
ledge of its cause. There are numerous beliefs commonly held in 
the absence of experiment, and wholly false, such as that adamant 
can be broken by goats' blood, that the beaver when chased throws 
away his testicles, that a vessel of hot water freezes more rapidly 
than one of cold, and so on. Experience is of two kinds : (i) that in 
which we use our bodily senses aided by instruments, and by 
evidence of tmstworthy witnesses ; and (2) intemal experience of 
things spiritual, which comes of grace, and which often leads to 
knowledge of earthly things. The mind stained with vice is like 
a msty or uneven mirror, in which things seem other than they are. 
Without virtue a man may repeat words like a parrot, and imitate 
other men*s wisdom like an ape, and all to no purpose. The in- 
tellectual effect of a stainless Hfe is well illustrated in the young man 
who is the bearer of this treatise. The degrees of spiritual experience 
are seven. (i) Spiritual illumination ; (2) virtue; (3) the gift of the 
Holy Spirit described by Isaiah ; (4) the Beatitudes ; (5) spiritual 
sensibility; (6) Fmits, such as the peace of God which passes 
understanding ; (7) states of Rapture 167-172 

CHAPTER II. 

It is solely by the aid of this science that we shall be able to dis- 

abuse men of the fraudulent tricks by which magicians have imposed 

on thenv As compared with other sciences, this science has three 

characteristics (' praerogativas '). Of these the first is, that it con- 



PART VL cxlix 

VOL. II. PAGES 

stitutes a test to which all the conclustons of other sciences are to be 
subjected. In other sciences the principles are discovered by experi- 
ment, but the conclusion by reasoning. An instance of this is 
afforded by the rainbow, and by other phenomena of a similar kind, 
as haloes, &c The natural philosopher forms a judgement on 
these things : the experimenter proceeds to test the judgement. 
He seeks for visible objects in which the colours of the rainbow 
appear in the same order. He finds this the case with Irish 
hexagonal crystals when held in the sun's rays. This propcrty, he 
discovers, is not peculiar to these crystals, but is common to all 
transparent substances of similar shape, similarly placed. He finds 
these colours again on the surface of crystals when slightly roughened. 
He finds them in the drops that fall from the rower*s oar, when the 
sun's rays strike them, or from a water-wheel, or in the moming-dew 
on the grass. They may be seen again in sunshine when the eye is 
half opened, and in many other cases 172-174 

CHAPTER III. 

The shape in which the colours are disposed will vary. Sometimes 
it is rectangular, sometimes circular 174 

CHAPTER IV. 

Armed with these terrestrial facts, the experimenter proceeds to 
examine the celestial phenomenon. He finds, on examining the sun's 
altitude and that of the summit of the bow, that the two vary inversely. 
The bow is always opposite the sun. A line may be drawn from the 
centre of the sun through the eye of the observer and the centre of 
the circle of which the bow is an arc to the sun's nadir. As one 
extremity of this line is depressed, the other is elevated. It becomes 
thus possible to compute the altitude of the sun beyond which no 
rainbow is possible, and also the maxlmum altitude of the bow. It 
will be found both by calculation and experience that this altitude in 
the latitude of Paris is forty-two degrees 175-178 

CHAPTER V. 

Still further investigating the shape of the iris, and the portion of it 
that can be seen, the experimenter conceives a cone of which the apex 
is the eye, the base is the circle of the iris, the axis being the line 
already described drawn from the sun's centre through the eye to the 
8un's nadir. In cases where this cone is very short, the whole of 
the base may be above the horizon, as may often be seen in the spray 
of a waterfalL In the sky however the cone is too elongated to admit 
of this : the base is bisected in various proportions by the planeof the 



cl ANALYSIS OF THE ' OPUS MAJUSJ 

VOL. II. PAGES 

horizon. The arcs visible are not portions of the same circle. When 
the sun is high, and a small arc is visible, it belongs to a larger circle 
than the arc seen when the sun is rising or setting. A bow can be 
seen when the sun is just below the horizon ; but owing to terrestrial 
vapours, only the crown of the arch is usually seen . . . 178-181 

CHAPTER VI. 

In some latitudes there can be no rainbow at noon even in the 
winter solstice. When the latitude (i. e. the distance from the zenith 
to the equator) is 24° 2$', the sun's altitude at noon in the winter 
solstice will be 42% therefore there can be no bow. Passing north 
from this latitude, there can always be a noon rainbow till we come to 
latitude 66** 25', when at the winter solstice there is no sun. Similar 
calculations can be made for other latitudes .... 181-185 

CHAPTER VII. 
We have now to inquire whether the iris comes from incident, 
reflected, or refracted rays. Is the bow an image of the sun ? Are 
the colpurs on the clouds real ? Why is the iris of circular form ? 
Here we call experiment to our aid. We find on trial that if we move 
in*a direction parallel to the rainbow it follows us with a velocity 
exactly equal to our own. If we approach it, it recedes: if we 
recede, it follows. The same phenomenon occurs with respect to the 
sun. We have seen that the sun is always opposite the rainbow ; the 
line between the centre of the bow and the centre of the sun passing 
through the eye of the observer. If the sun were apparently 
stationary, this would involve the bow moving much faster than the 
observer, the latter moving through the same angle, but at less 
distance from the apex. But this is not so. * Therefore there is an 
apparent motion of the sun concurrently with that of the bow. The 
case is analogous to what happens when a hundred men are ranged 
in line facing the sun. Each sees the sun in front of him. Their 
shadows seem parallel, though we know that in reality they must 
diverge, yet owing to the vast distance of the sun this divergence is 
imperceptible. We are thus brought to the condusion that, supposing 
a rainbow to occur, each of the hundred men, facing backwards, 
would see a different rainbow, to the centre of which his own shadow 
would point. The rays causing the iris are therefore not incident 
rays, otherwise the colour would appear fixed in the cloud. And for 
the same reason they are not refracted rays, for in refraction the 
image does not follow the change of place of the observer, as is the 
case here. One condition of the phenomenon is that the atmosphere 
shall be more iUuminated at the standpoint of the observer, and less 



PART VI cli 

VOL. II. PAGES 

at the position of the cloud. Tbe movement of the sun from east 
to west during the appearance of the rainbow may be left out of 
account 185-190 

CHAPTER VIII. 
The colours in the bow arise from an ocular deception. They are 
analogous to those which appear when the eyes are weak orhalf-shut. 
They are not due to the same cause as the colours produced when 
light shines through a crystal, since these do not, like the colours of 
the rainbow, shift with the position of the observer . . . 190-192 

CHAPTER IX. 

Each drop of rain in the cloud is to be regarded as a spherical 
mirror; these being small and close together, the effect is that of 
a continuous image rather than of a multitude of images. The colour 
is due to the distortion of the image caused by the sphericity of the 
mirror * 192-193 

CHAPTER X. 
The diversity of colours has been attributed to varieties in the 
texture of the cloud, the denser parts producing violet and blue, the 
lighter parts red and orange. But we see the same colours in the dew- 
drops, where there can be no such differences of density ; similarly in 
the crystal. Aristotle has been wrongly translated and interpreted 
in this matter. Another erroneous belief is that lunar rainbows occur 
only once in fifty years. They may occur at any fuU moon under 
suitable atmospheric conditions 193-194 

CHAPTER XI. 
The shape of the bow is a difficulty. It cannot be explained by 
refraction. It is to be observed that the same colour is continued all 
round the circle in each ring. All parts of the ring therefore preserve 
the same relation of the solar ray to the eye. This implies circularity 
of form. It is asked why the whole space contained by the cirde is 
not occupied with colour. Because from the points in this central 
area rays equal to the angle of incidence are not refiected to the 
eye 194-196 

CHAPTER XII. 

The cloud therefore is not coloured ; the appearance of colour, for 

it is only an appearance, is given by rays reflected from the raindrops. 

Of colours there are five, white, blue, red, green, black : though 

Aristotle, dividing blue and green into other shades, speaks of seven. 



^ 



clii ANALYSIS OF THE ' OPUS MAJUS: 

VOL. II. PAGES 

These colours appear to have some relation to the various structures 
of the eye. In addition to the problem of the rainbow, there is the 
problem of haloes and coronae. On this I give the best explanation 
that as yet occurs to me. I do not however pretend that it is satis- 
factory. Far more careful experiments, made with properly con- 
structed instruments, are needed before an adequate explanation 
can be given * 196-201 



The Second Prerogative of Experimental Science . 202-215 

In all sciences Experiment is able to reveal truths quite un- 
connected with the discussion of principles, and with regard to 
which it is useless in the first instance to assign a reason. The 
initial state of mind should be readiness to believe; this should be 
followed by experiment : reasoning should come last. I subjoin 
examples of my meaning. 

1. The astronomer constructs his spherical astrolabe, by which he 
can observe the precise longitude and latitude of heavenly bodies 
at different times. But it is not inconceivable that experiment may 
devise means of bringing this instrument into such relation with 
the revolution of the heavens that it should follow their course. The 
motion of the tides, the periodic changes in certain diseases, the 
diumal opening and closing of flowers, are facts tending to belief 
that such a discovery is possible. If effected it would supersede all 
other astronomical instruments 202-203 

2. My next example relates to the act of prolonging human life. 
As yet we have nothing to rely on but ordinary rules of health. 
These are obser\'ed but by few, and usually not till the close of life, 
when it is too late. If a suitable regimen were observed by all, 
no doubt life would be much prolonged. But there are special 
remedies unknown as yet to medicine, but to be found by experiment, 
which may extend the period of life much further. Observation of 
the habits of certain animals may guide us to truths on this matter 
which are as yet hidden. Other indications are given in the works 
of Aristotle, Pliny, Artephius, and others. A combination of gold, 
pearl, flower of sea-dew, spermaceti, aloes, bone of stag's heart, flesh 
of Tyrian snake and of Aethiopian dragon, properly prepared in due 
proportions, might promote longevity to an extent hitherto un- 
imagined 204-208 

3. A third example may be found in Alchemy. The problem here 
is not merely to transmute the baser into the more precious metals, 
but to promote gold to its highest degree of perfection. In this 
perfected gold we should probably have a further aid to the prolonga- 
tionoflife 214-215 






PART VIL cliii 

vol. ii. pages 
Third Prerogative of Experimental Science . . 215-222 

In this we leave altogether the domain of thc sciences now re- 
cognized, and open out entirely new departments of research. At 
present the inflaences exerted on us by the stars can only be known 
through difficult astronomical calculations. Experimental science 
may enable us to estimate them directly. It may be possible for us 
to act on the character of the inhabitants of any region by altering 
their environment. Inventions of the greatest utility may be dis- 
covered, as perpetual fire, or explosive substances, or modes of 
counteracting dangerous poisons, and innumerable other properties 
of matter as yet unknown for want of experiment. The Magnet, of 
which use is already made, is but a type of other mutual attractions 
exerted by bodies at a distance. For instance, if a young sapling be 
longitudinallydivided and the two divisions be brought near together, 
held each by the middle, the extremities will bend towards each other. 
In conclusion, I may point out the influence which the possessors 
of this sdence may exercise in the promotion of Christianity among 
the heathen, whether in subduing their pride, in disabusing them 
of false beliefs in magic, or in overcoming their material force . 215-222 



PART VII. 

MORAL PHILOSOPHY 223-404 

FiRST Part of Moral Philosophy 223^-249 

We have now considered Philology, Mathematics, and Experi- 
mental Science, and have seen their intrinsic importance, and their 
value to the Church. I come now to a fourth science, which stands 
on a higher level ; that which relates to the practical conduct of life. 
Other sciences relate to action of various kinds ; but this to those 
actions by which we become good or bad. It is the science which 
instructs Man as to his relations to God, and to his neighbour and to 
himself. It deals therefore with the final purpose of all human 
wisdom. It is closely related to Theology, to which it supplies 
important aid, sharing therefore its dignity. Proceeding to the 
divisions of the subject, the first point to note is tliat the condusions 
of the previous sciences form the principles of ethical science. The 
others have prepared the way for this science as their mistress. We 
find ethical principles everywhere difiused through them, which are 
now by this highest of the sciences to be gathered together and find 
VOL. I. 1 



cHv ANALYSIS OF THE * OPUS MAJUS! 

VOL.II. PAGES 

their proper place. It is called by Aristotle Moral Science; by 
others Civil Science, as laying down the obligations of citizens and 
states; the city standing in old times in the place of the modem 
state or empire. It falls under two divisions : first, the establish- 
ment of laws of conduct ; secondly, exhortations towards their 
fulfilment 223-225 

The first division consists of three parts : (i ) duty to God ; (2) duty 
to our neighbour ; (3) duty to ourselves. These three divisions are 
indicated both in the Old and in the New Testament. We may 
begin by laying down certain principles either held by this science in 
common with Metaphysics^ or reached through metaphysical methods 
which here would be out of place. These are, (i) that God exists ; 
(2) that He is naturally known to man ; (3) that He is of infinite 
power and wisdom ; (4) that He is One ; (5) that He is also Trine ; 
(6) that He is the author of Nature ; (7) of angelic substances ; 
(8) of human souls ; (9) these are immortal; (10) the highest good 
is in the future life; (11) man*s capacity for this good; (12) the 
moral govemment of the world ; (13) future rewards and punish- 
ments; (14) the worship of God ; (15) man's duty to his neighbour 
and to himself; (16) the need of revelation ; (17) of mediation ^ 
between God and man 225-228 

There are other principles of which Metaphysics can take no 
cognizance— relating to the nature of God and the angels and tofuture 
life. Of these the first is the Triune nature of God. Something of this 
has been revealed to the ancient philosophers, having been received by 
them from the patriarchs, as explained in the second part of this 
work. Plato and Porphyrius are instances of this ; examples may be 
found also in Aristotle and Avicenna 228-232 

The mutual relations of the three Persons of the Trinity constitute 
the first foundations of Moral Science. Next to this is the Incama- 
tion. Here too many traces of knowledge of the truth are discover- 
able in the ancient philosophers, both Greek and Arabian. There are 
also facts in natural history pointing in the same direction . 232-234 

The coming of Antichrist is also an article of faith, of which some 
knowledge is to be observed in the writings of Greek and Arabian 
philosophers, and which some have thought is to be fulfilled in the 
actual Tartar invasions, though this is uncertain. It will be followed 
by the final punishment of the Evil one 234-235 

The creation of the world and of the human race is also a principle 
laid down in the writings of Aristotle, Albumazar, and others. We 
find also the doctrine of the existence of angels, good and bad. The 
former direct the motions of the heavenly bodies ; and one of these 
is specially attached to the destiny of each human being as his 
guide through life. Bad angeb may tempt him to evil • . 235-238 



PART VIL clv 

VOL. II. PAGES 

Of the immortality of the soul much is to be found in Aristotle, 
Plato, Cicero, Hermes Mercurius, and Avicenna ; and they were not 
ignorant that the body must be regarded as inseparable from the 
soul. They had knowledge also of a future state of rewards and 
punishments ; though, as Avicenna insists, the cares, enjoyments, and 
occupations of this world hide this knowledge from us. In shaking 
ofif these earthly trammels and receiving spiritual enlightenment true 
wisdom consists, which Aristotle in the sixth and tenth book of his 
Ethics holds up as identical with true happiness. Theophrastus his 
successor, and Cicero, confirm what he has said. Thus that highest 
good of which Aristotle speaks consists in participation of the life of 
God. Nor were the ancient philosophers unaware of the future 
misery that awaited the bad, as the writings of Socrates, Cicero, and 
Hermesshow . 238-246 

We now pass to the obligation to worship God, in thankfidness 
for our creation, in reverence for His infinite i>ower, in consideration 
of our future bliss. On these points Avicenna^ Porphyry, Plato, and 
Cicero have spoken explicitly. St Augustine has accepted Cicero's 
explanation and definition of religion. Avicenna has compared our 
approach to the presence of God to our entrance into the presence- 
chamber of a great king. And Hermes has enlaiged eloquently on 
this subject. As to the ceremonies of heathen nations, they were for 
the most part superstitious and useless, and there is no need to dwell 
upon them. Thcy were practised by these ancient writers not for 
their intrinsic value, but in order to conform to popular prejudice 
and custom 246-249 



Second Part: Civic Moralitv 250-263 

CHAPTER I. 

The first subject under this head is the regulation of the propagation 
of the race by the iaw of marriage. Next comes the subordination 
of ranks, both in the state and in the family. Thirdly, the appoint- 
ment of educators and judges. A definite position and function 
should be allotted to each citizen. Provision should be made for the 
treatment of criminals, and for the replenishment of the treasury. 
Laws must be made for testamentary dispositions and for contracts of 
all kinds. Occupations injurious to the state must be prohibited. The 
defence of the country by an oiganized force must be secured . 250-252 

CHAPTER II. 
It is liirther necessary that orderly succession in the govemment 
sbould be arranged* The ruler should choose his successor with tbe 

] 2 



clvi ANALYSIS OF THE • OPUS MAJUS: 

VOL. II. PAGES 

consent of hb nobles and of the people. Any subsequent pretender 
should be outlawed. These are the principal divisions of the subject ; 
which however indudes the whole of Civii Law as received among 
the Latins, to whom the Greeks transmitted it . . . • 252-253 



Third Part: Personal Morality 254-365 

CHAPTER I. 

This third division is subovdinate to the two preceding. Our duty 
to God occupies of course the first place. Secondly comes public 
good; which takes precedence of private good, as Aristotle has 
maintained. Love, Peace, Justice fall in this second division. Man 
is a social animal. A hermit living by himself is neither good nor 
bad. We are bom to make our lives useful to others, as Cicero, 
Seneca, and the Stoics have so often said. On the subject of 
personal conduct and character admirable truths have been laid 
down by heatfaen writers, which may put Christians to shame. 
We will begin with those relating to virtue and vice in general; 
passing afterwards to special branches 254-255 

CHAPTER IL 

Aristotle has defined two kinds of virtue. The first consists in the 
subordination of feeling to reason ; to this the name of moral virtue 
is appropriated. In his Ethics he has spoken of twelve moral 
virtues, each regarded as the mean between two opposite vices. 
These are fortitude, chastity, liberality, munificence, magnanimity, 
public spirit, gentleness, friendliness, sincerity, gaiety, modesty, 
justice. The second kind of which Aristotle speaks is virtue of the 
Intellect. Its branches belong to the region of speculation, exoept 
so far as they are directed to the knowledge of divine things, or of 
matters useful to the state. Aristotle has distinguished innate from 
acquired virtue. All the philosophers of antiquity speak of virtue as 
the only real good, notably Seneca, Apuleius and Cicero, and have 
also insisted on the inconsistency of those who theorize about virtue 
without practising it They have spoken of it as the beauty and the 
health of the soul, and have pointed out that it is only to be acquired, 
by long and arduous practice. By this means even inveterate vices 
may at last be eradicated 255-262 

CHAPTER IIL 

The ancients have spoken of vice in the same spirit as of virtue. 
Algazel has said that vice acts on the soul like nist on a polished 



PART VII. clvii 

VOL. II. PAGES 

mirror, hindcring thc pcrception of the highcst truth. Sin blinds thc 
soul ; and hence the view of Socrates that evil actions result from 
ignorance. There is a natural shame at sin for its vileness ; a con- 
sciousness that it lowers to the lcvel of the beasts, each race of whom 
typifies some one among human vices. We take our tone from those 
around us for good or evil : hence it is of the utmost moment with 
whom we associate. This truth also is illustrated by the lower 
animals, as Boetius has pointed out. Much importance is attachcd 
by Seneca and others to self-examination at the close of each day, as 
to the control or the encouragement that has been given to vicious 
impulsc. Such control, as Aristotle and Seneca insist, should be 
exercised from childhood 262-266 



CHAPTER IV. 

From virtue and vicc in general we pass to special virtues and 
vices. Wc find that the teaching of ancient philosophers relates to 
Avarice, Pridc, Lust, Gluttony, Anger, Envy, and Sloth — in other 
words, to the seven mortal sins. Of these, all but one, Anger, relate 
to pleasure and prosperity; Anger only has to do with adverse 
circumstances. Let us begin with the former class. Disregard of 
wealth was preached and practised by Aristotle and a long series of 
philosophers. Seneca and Ptolemy have pointed out that this earth 
is but an infinitesimal part of the universe, and that the disputes of 
contending nations for its possession are like the quarrels of ants for 
an anthill. Apulcius, in his study of Socrates, has insistcd strongly 
on the distinction between the inner man and the casual accidents of 
health, strength, or wealth that surround him. Sallust and Seneca 
have spoken of the general corruption that has foUowed the pursuit 
ofwealth 266-270 

CHAPTER V. 

As to sexual desire, Archytas and Cicero have said much of its 
disturbing influence on reason. Aristotle in his exhortations to 
Alexander dwelt on this, and on the degradation of man through 
lust to the level of the brutes. Seneca and Cicero have dwclt on 
thc same subject. On Gluttony and Drunkenness, Seneca has 
enlarged in his discourse to Helvia, and in his other lettcrs. He 
speaks of it as throwing the door open to lust, cruelty, and other 
vices. Cicero quotes a letter of the philosophcr Anacharsis upholding 
the advantage of simplicity of life. Plato, Avicenna, and others have 
said much of the necessity of setting the miud free from the trammels 
ofthebody 270-275 



clviii ANALYSIS OF THE ' OPUS MAJUS: 

CHAPTER VI. 

VOL. II. PAGES 

Having spoken of the vices connected with pleasure and pros- 
perity, we pass to the discomfiture of the soul in adversity by Anger. 
In resisting anger, the first step is to see it as it really is, with all its 
disastrous consequences to spiritual and temporal welfare. By nature 
man is mild and gentle, inclined to help his fellow-man. Giving way 
to anger he exhibits the physical symptoms of wild beasts, distortion 
of the countenance, agitation of the limbs,swelling of the veins,foaming 
at the mouth, gnashing of the teeth, spasm of the breath. The effect 
on the rational faculties is no less disturbing. It has oflen utterly 
destroyed the mental balance, and the temporary insanity caused by 
it has become p^rmanent. No less pemicious is its efTect on practical 
conduct. All the virtues are inter-connected, so that the loss of one 
involves injury to the rest. Anger is destructive to the noblest 
virtues, such as clemency, magnanimity, pity, natural affection, tran- 
quilJity and joy. Clemency is specially characteristic of man, and to 
the rulers of men it is peculiarly appropriate* It may be noted that 
among bees the king alone is without a sting. The noblest of the 
Roman emperors have been distinguished for this virtue. Closely 
connected with it is the virtue of magnanimity, which leads its 
possessor to forgive injuries, and to be unconscious of their existence. 
But this state of mind is wholly incompatible with anger. As that 
part of the heavens which is nearest the stars is free from clouds, so 
is the magnanimous spirit free from the disturbing influences of 
anger. The swelling and exaltation of spirit which anger produces 
is no sign of vital energy, but rather of morbid flatulence and weak- 
ness. Besides magnanimity, other virtues are impaired by anger, as 
mcrcy, patience, and joy. Mercy is that which lifts man nearest to the 
level of God. Nothing is nobler than forgiveness and forbearance, and 
reddiness to find extenuating circumstances in every ofTence, remem- 
bering how prone we are to give offence ourselves. To avenge 
ourselves on brute animals is what no one thinks of : and should we 
be less indulgent to men than to brutes? Readiness to forgive a 
personal injury is stimulated by cultivating indulgent feelings towards 
human nature. But such a state of mind as this is wholly incom- 
patible with anger. The destructive effects of Anger on such virtues 
as Piety and Peace are too obvious to dwell upon . . . 275-288 

CHAPTER VI I. 

In addition to these things, anger makes a man reckless of his own 
life and that of his friends, as there are many signal examples in 
history to show. Under its infiuence a man becomes careless of 
wealth or reputation, and is led to blasphemous rebellion against 



PART VIL clix 

VOL.II, PAGES 

Providence. It differs from the other vices in the suddenness of its 
access, and in its overthrow of the mental balance. Moreover it 
spreads by contagion through whole populations, and vast regions 
have been devastated by it • 288-290 

CHAPTER VIII. 

Examples of self-restraint. In contending against this vice, it will 
be useful to recall the examples of those who have succeeded in over- 
coming it. Sociates is one of the most striking of these. Plato is 
another. Of Archytas, Xenophon, Diogenes, Democritus, Heraclitus, 
similar facts are recorded. Kings and rulers have shown the same 
self-mastery. Antigonus dealt indulgently with those whom he over- 
heard speaking ill of him. Philip of Macedon forbore to punish an 
Athenian ambassador who had grossly insulted him. £ven Alexander 
Gould at times restrain himself. Pisistratus and Cato may also be 
mentioned, and the behaviour of Augustus to Timagenes should not 
beforgotten 290-294 

CHAPTER IX. 

We now pass to the direct remedies against this vice. One is the 
resolution to inquire into the facts of the case before we give way to 
anger. We should wait, and we should demand sure evidence of the 
injury. We should guard against the su$picious temper, against 
readiness to take offence, and not aUow, as so often happens, anger 
to be its own evidence. We should beware of expecting too much 
from our friends. To Caesar his friends were more fatal than his 
enemies, on account of the unreasonable expectations which they 
had founded on their friendship. The second remedy is to insist on 
delay before punishing an offence, so that the angry mood may pass, 
and meanwhile to restrain every extemal sign of anger, whether in 
voice or gesture. This was always the habit of Socrates. Meanwhiie 
every effort should be made to find excuse for the alleged perpetrator 
of the wrong. Finally, it should always be remembered that the 
injurer is a fellow-citizen, or at least a member of that greatest of 
commuiities, the human race. The offender is either an equal, an 
inferior, or a superior. In each case there is a special ground for 
refraining from revenge. The enormity of the ravages resulting from 
this vice is my excuse for dwelling upon it at such length . . 294-298 

CHAPTER X. 

From the subject of Anger I pass to that of patient endurance of 
misfortune. And first, since there is a moral govemmentof the world, 
why do good men sufier ? Seneca in his essay on this point says 



clx ANALYSI3 OF THE * OPUS MAJUS: 

VOL. II. PAGES 

that God sends these safrerings to strengthen their character. In 
the training of children the father has more regard for vigour of 
character than the mother, and acts accordingly. So it is with God. 
Those whom He loves He chastens, lest through ease and comfort 
their forces should decay. There can be no proof of heroism except 
wrestling with calamity, therefore those are to be pitied who have no 
such trial of their force. A brave man is proud that his general sends 
him to the post of danger. The sailor, the ploughman, are hardened 
by their calling : and it is so with character. Brave men face their 
trials willingly, and are purified by them as gold in the fumace. 
Thus the true blessings of life are g^ven ; the false appearance of 
happiness is seen for what it is, a superficial veneer veiling the vice 
and worthlessness within 298-303 

CHAPTER XL 

Seneca proves further that the wise man cannot sustain injury or 
insult. That he will be attacked is certain, but he will not give way 
to attack ; it will not injure him ; he will be as asbestos in the flame 
or rocks in the sea-foam. We may distinguish injury from insult ; 
the former being the graver, though the latter is often more dreaded. 
The injurer seeks to inflict hurt. But for the wise man there is no 
hurt but sin. What is extemal, what is inflicted by fortune, cannot 
touch him. He can lose nothing : for what is truly his own he carries 
with him. It may be urged that such a man is impossible. Rare he 
is doubtless: but Cato proves the possibility. Injury can only be 
inflicted by the strong on the weak ; and how can the bad man be 
stronger than the good ? Obviously the bad man may intend a 
wrong : but it does not follow that the wise man will suffer it. He is 
beyond the reach alike of injury or benefit ; he is raised to the level 
of God, except that he is mortal. He bears all assaults gladly, looking 
on them as trials of his strength. Insult is a smaller matter, to be 
complained of rather than avenged. It implies some mistrust in the 
recipient of his own worth, from which a wise man would be free. 
We are not to suppose him insensible. Bodily pain, the loss of friends, 
political disaster, he will feel like other men ; but of mere insult he 
will be simply unconscious, or will treat it as a passing dream. He 
will not take oflence at it any more than a mother at the petulance 
of her child. For those who would insult him are but grown-up 
children. If he restrains and punishes them, it is not because himself 
has been hurt, but for their own welfare. The physician is not angry 
with his delirious patient. If rich men pass him by unnoticed, he 
reflects that they are but beggars or worse, since the beggar wants 
little, they much. It would be doing them too much honour to be 
offended by them. The current of opinion is nothing to him : he 



PART VII. clxi 

VOL.II. PAGES 

passes on athwart it, as the planet moves against the revolution of 
the sky. He makes no distinction of what can be tolerated and what 
is intolerable. He must conquer fortune wholly or not at alL For 
the wise man such a thing as injury does not exist If he deserves 
what he suflfers, he takes it as a judgement : if not, let the doer 
blush for it Such was the spirit of Sooates .... 303-311 

CHAPTER XII. 

In a discourse addressed to his mother> Seneca has suggested 
consolation under every kind of calamity. When misfortunes are 
many, it is not worth while bewailing any one of them separately. 
We aie hardened by the rett, like veteran soldiers who bear their 
wounds in silence. Seneca all^es his own example under triaL 
Though not attainingto thelevel of thetruly wise, he yet has followed 
wise men's teaching, and so has been forewarned and forearmed 
against the caprices of fortune. Take each misfortune singly. And 
first of exile. What is exile but a change of place ? Of the vast 
multitudes in Rome is not a large proportion foreign ? Again, is not 
constant motion as natural to the mind as it is to the heavenly 
bodies ? Looking at the human race, we find each part of it constantly 
migrating ; and what is migration but exile ? Wherever we go we 
carry our moral nature with us : we find the same universe around us. 
Let us remember what Bnitus tells us of the cheerful activity of 
Marcellus in exile. Poverty is sometimes added. If meat and drink 
and clothingare supplied, it is no cause for complaint that avarice and 
gluttony are not satiated. The real necessities of life are easily 
provided. For the rest, the mind is everything; jewels, gold and 
silver are of small account. Violence and disease may affect the 
body ; the mind they cannot touch. The poor are not less happy 
than the rich. But luxury has been carried so &r that the travelling 
money of an exile is what oncfc would have been the patrimony of 
princes. Homer had but one servant, Plato three, Zeno none. But 
how if all these evils, poverty, exile and neglect, be joined together ? 
The answer is the same. The same reason which supplies endurance 
of one wtll suffice for alL As for ignominy, it depends on him who 
endures it : the prison was an honourable p!ace when Socrates was 
its inhabitant. When a great man is cast down he is venerated 
still, as when a stately temple is laid in ruins .... 811-817 

CHAPTER XIII. 

Writing to Gallio, Seneca asks, Is death an evil ? All men share it. 
Do men speak ill of you ? What, if they are bad men ? You are in 
pain. If the pain is slight it is easy to bear, if severe the greater 



clxii ANALYSIS OF THE ' OPUS MAJUS' 

VOL.II. PAGES 

honour in bearing it. It is hard to be poor. All depends on who is 
the poor man. The birds and beasts do not feel their poverty. The 
rich man is but a money-chest. The crowds that follow him are 
but as flies looking for honey, or wolves round a carcass . 318-319 

CHAPTER XIV. 

Writing to a lady who had lost her son, Seneca continues, The 
mastery of life is only to be seen when trial tests it. Your son 
stood this test nobly. Natural affection has its natural limits. The 
grief of animais for the loss of those dear to them lasts but a short 
time. Men alone grieve long ; and even with them it is the weaker 
sex, or the more barbarous tribes, who are crushed by it Was this 
sorrow unexpected by you ? Remember that none are exempt from 
it. Of no earthly possession have we a secure hold. We have them 
as actors have their stage properties ; the scene ended, they pass 
back to the manager. What we have we should be ready to give 
up at a moment's call. In loving it think of it as even now passing 
away. Why weep one part of life when the whole of it is sad ? Man 
is but a frail helpless thingthat the most trivial accidents may destroy. 
His longest life is but a few years, and may be cut short at any 
moment. There are noble instances of constancy under such 
calamities as yours, as of the priest engaged in sacrifice who, hearing 
of his son's death, went on calmly with the service. Comelia, mother 
of the Gracchi, Livia and Octavia the sister and the wife of Augustus, 
bore their bereavement nobly. Refiect further that life is so un- 
certain that the sudden close of it may mean avoidance of calamity 
which would otherwise have foUowed. Nothing is sure but what has 
been already done. The sooner we are disentangled from earthly 
things the speedier will be our flight to the realms above . . 319-322 

CHAPTER XV. 

My reasons for treating this third part of Moral Philosophy at 
such length are two. First, that although we are far in advance of 
heathen nations in knowledge of spiritual life, we are far behind them 
both in word and deed, as to public and private life in this world. 
Secondly, the works of Seneca from which I quote have been hitherto 
unknown to me, in spite of a long search for them, and probably to 
others 322-323 

CHAPTER XVI. 

I proceed therefore with selections from his Essay on the Brevity 
of Life. Men complain that life is short It would be long enough if 



PART VIL clxiii 

VOL. II. PAGES 

they spent it wisely. But they waste it like spendthrifts, in luxury, 
vice and sloth, or at the best in restless activity. Men cherish 
a dream of retirement and quiet reflection at the close of life. But 
they put off realizing it till too late. We know how Augustus longed 
for such a time of peace. The art of life is no easy matter to be 
leamt in a moment. Life itself is not too long for it The wise man 
knowing this guards his time against the encroachments both of 
pleasure and business. Thus whatever his span of life he truly lives. 
For length of years is no proof of life. The shipwrecked sailor, tost 
hither and thither, has not made a voyage. Men crave for life when 
they see the end of it at hand. But while it lasted they lavished it 
recklessly. Much too is wasted in schemes for the morrow, the 
immediate work before us beingleft undone. Time must be seized 
as it flies. Of the three parts of time, past, present and future, the 
first alone is our inalienable possession. Yet how few care to look at 
it. The ambitious, cniel or intemperate man hates his memories. 
The one part of life which is really his own he flees from ; and yet 
men cling to life when it threatens to escape them. Few understand 
what true leisure is. Most men'5 pursuits even when hannless are 
but laborious futility. Leamed men occupy themselves with the 
collection of trivial and useless facts : [though be it said in passing 
that sometimes these facts have philolog^cal interest ;] wise men have 
the whole expanse of history open to them. They can escape £rom 
the littleness of the present to companionship with the great thinkers 
and teachers of past ages. AII time belongs to such men. They 
recall the past : they act in the present : they arrange the future. 
They see things to which other men are blind, and they escape. 
other men's miserable anxieties as to what may befall them. It is 
well therefore to spare a few years for quiet meditation before our 
faculties are enfeebled 323-333 

CHAPTER XVIL 

It is well for us not to be exempt from the common lot. Great 
wealth is great slavery. Life at the best is but a stormy voyage, and 
the only haven is death. Life has been lent us ; let us retum the 
loan ungrudg^ngly. And for the death of those dear to us, though we 
must feel like men, let us also bear like men .... 333-335 

CHAPTER XVIII. 

I now pass to Seneca's discourses on the Blessed Life, and on Peace 
of Mind ; for they are well adapted to strengthen the spirit and render 
it careless of outward prosperity. Men wish for happiness, but know 
not where to find it. It is worse with them than with travellers who 



clxiv ANALYSIS OF THE * OPUS MAJUS: 

VOL.II. PAGFIS 

have lost their way. These can be set right by natives of the plaoe. 
But in Hfe it isthe broadest and most trodden road that leads 
farthest astray. We must leave the crowd if we would go right. We 
must look within ; the mind must be a law to itself. Nature must be 
our guide. If our mind is attuned to nature it will not fail us. We 
shall thus substitute for the distractions of pieasure and fortune the 
joy and tranquillity of inward peace. He is to be called truly blessed 
to whom the only good or evil is good or evil of the soul, the only 
pleasure, to be free from slavery to pleasure. Virtue is undying, 
pleasure perishes in the act of fruition. Pleasure may be the lot of 
good men and of bad : but for the good it is a servant, not a master ; 
they are undisturbed by its absence; like the universe, like the 
Deity, they retain self-mastery. They live and act without strife, 
without vaciilation, in inward harmony and peace. Yet virtue is not 
to be sought for the joy that it brings, any more than fields are tilled 
for the flowers that may spring up amidst the com. It is an end in 
itself ; there is nothing beyond it. With vicious pleasure virtue is 
incompatible. Lawful pleasures it accepts, as using but not abusing 
them. Unless raised above them, the wise man could not withstand 
the trials of life. Pleasure is but an addition to his life, not the 
goveming principle. To confound these things, to regard pleasure and 
virtue as inseparable, is a fatal error, leading inevitably to the triumph 
of the baser element. There must be no compromise. The highest 
good ceases to be the highest if mixed with something alien to itself. 
The very foundation of virtue is undermined when it is made to 
depend on outward circumstance. It will no longer inspire deeds of 
heroism and self-sacrifice. When such are called for, they wiU be 
done unwillingly, and not with the prompt obedience of the faithful 
soldier. The reward of our fidelity is true freedom. Nothing can be 
done to us against our will, for our will is at one with that of God. 
But who, it may be asked, comes up to this standard ? whose life is 
not utterly inconsistent with it ? Admit this, and yet we need not be 
deterred from aiming at it. It is best to have high aims. If we 
resolve to be fe^rless in the presence of death, not to be the slaves of 
fortune, to acknowledge our bond to our fellow-men, to act when 
alone as though the world beheld us, to set restraint on appetite, to 
bow in all things before God's will, we are at least on the upward 
path, though we may not attain. Those who scofT at us will profit little. 
A man may be wealthy and prosperous, yet good. He may use his 
wealth to relieve the needy or to support the state. He will not 
throw it away ; yet, if it be taken from him he will be content. The 
difference between him and others is. that his riches belong to him, 
they belong to their riches. If innocently gained they cause him 
neither pride nor shame. He will hold them lightly, and will use 



PART VII. clxv 

VOL. II. PAGES 

thcm woithily. We must distinguish between those who are strug- 
gling towards true wisdom, and those who have attained it. We can 
at least resoive not to bow down before wealth as a blessing, not to 
be the slaves of it, always to hold ourselves in readiness to abandon 
it. Strange indeed is the tendency in bad men to malign men better 
than theniselves, instead of attacking one another ; to pick out the 
specks in these, heedless of their own hideous eruptions. Yet 
they only bring into greater prominence the virtue which they 
assault 835-347 

CHAPTER XIX. 

We must pursae our steady course, not diverted from it by the 
varying blasts of opinion. We shall incur the reproach that a philo- 
sophic life involves abandonment of the duties of a citizen. But in 
retirement we remain active, still working at what will be of use to 
those who come after us. The turbulent politics around us are not 
our only field of action 348-349 

CHAPTER XX. 

I condude with extracts from Seneca's discourse on Peace of Mind, 
without which there can be no happiness. We are as ready to flatter 
ourselves as others. We are too timid to tell ourselves the truth. 
Yet without uprooting our secret vices there can be no inward peace. 
Sometimes we yield to the desire for incessant change ; sometimes 
we sink into inertness. Or we have not attained full mastery over our 
passions, and are kept in perpetual struggle ; or again we are still tor- 
mented by ungratified ambition. These disappointed hopes prey on 
the mind, ahd we become envious of the success of others. We shift 
and tum in hope that change may bring relief, we lose all power of 
forbearance, and end with disgust for life and the world. The remedy 
for this is not, as Athenodorus advises, to re-enter the arena of public 
life, but to choose such occupations in retirement as shall make our 
lives useful to others. We may serve the state by advising and 
directing the young, as well as by holding public offices. We are not 
to flee from men and live only for ourselves. We remain citizens ; 
but of the world, not merely of a single state. We act on those 
around us by the influence of example. Socrates under the Thirty 
Tyrants was a tower of strength to his fellow citizens. It is well 
carefully to measure our own powers, which we are apt to overrate. 
Defects of temper, health, fortune, often unflt us for public life, and 
point to retirement as the better course. We should not beg^n what 
we cannot carry through. Great care should be taken in the choice 
of friends ; not insisting on perfection, but above all avoiding the 



clxvi ANALYSIS OF THE * OPUS MAJUS: 

VOL. II. PAGES 

qucnilous. Consider nert thc question of wealth, perhaps thc most 
fruitful sourcc of our miseries. The less wealth we start with the less 
we can lose : and the rich bear losses quitc as badly as the poor. Of 
this Diogenes was well aware, when he took to a life of voluntary 
poverty. There can be no more doubt of his happiness than of the 
happiness of God. When his one slave left him he merely remarked 
that if the slave could do without him surely he could do without the 
slave. Our wisdom is to reduce thc number of our wants, to be 
content with a moderate fortune, and to live well within it Even in 
intellectual pursuits there should be the same moderation. Vast 
collections of books are of small avail, monuments of luxury rather 
than aids to study. In all the perplexities of life courage iirst, then 
custom, will teach us to bear the yoke. Custom is nature's sovereign 
remedy for all cares and sorrows. Life, whatever its station or 
degree, is a servitude. Custom adapts us to it and we ceasc to com- 
plain. Let us leave the unattainable, and attempt things within our 
reach. The lofly are liable to the deepest fall. These counsels are 
for ordinary men, not for the man of perfect wisdom. For he can walk 
more boldly : to him not fortune only, but his own life, is but a tem- 
porary loan, which he is ready to surrender at call and gratefully. The 
test of a good life is readiness to die. Knowing that he was bom into 
a world of trouble, no evil can take him unawares. Let us avoid the 
crowds of men who rush hither and thither like insects on the trees 
in restless and purposeless activity. Idle conversation is apt to be 
worse than idlc. Let us refrain from too many occupations; our 
disappointment will be the less. Let us take the work that comes to 
us, neither too eager nor too fickle. Let us possess our souls in 
patience, all else being external to us and indifferent. The bchaviour 
of Theodorus the philosopher, and o{ Canus Julius when sent to his 
death by Caligula, are noble examples. Further, we must not indulge 
in too much grief at the errors of mankind. Laughter is more to the 
purpose than indignation ; though calm observation is a better attitude 
than either. Nor need thc painful death of brave men afflict us, since 
they themselves endured it gladly 349-362 

CHAPTER XXI. 
Since thc body acts upon the mind, time for relaxation and 
recreation must be given. Saintly men have always admitted this 
and practised it, following the cxample set by St. Bencdict. Seneca, 
to whom much divine truth has been revealed, has insisted on this 
point strongly. We must not always be alone, he says, nor always 
in a crowd. There must be a change of occupation; occasional 
amusement and gaiety. Hours of work must be limited ; exercise in 
the open air, occasional change of scene, are good ; even indulgence 



PART VII. clxvii 

VOL. II. PAGES 

in wine is not to be wholly forbidden. The mind is stirred by such 
influences and raised above its usual levei. To these may be added 
the inspiring influence of music, of which the prophet Elijah availed 
himself 362-365 



MORAL Philosophy : FOURTH Part . . . . 366-404 

The beauty of the subject, and the rarity of the books treating of it 
explain the length of the preceding part. I now pass to the grounds 
for accepting the Christian religion, which points the way to happiness 
in a fiiture life, and thus gives a meaning and a purpose to moral 
philosophy. God has never left men without the means of salva- 
tion ; hence we find ancient philosophers, and especially Aristotle, 
considering what are the principles which preserve or destroy 
states 366-367 

The religions now existing in the world are those of Saracens, 
Tartars, Pagans, Idolaters (Buddhists), Jews, Christians. They 
are distinguished not merely by opinion, but also by difference 
of moral aim. The Saracens permit excessive indulgence in sexual 
pleasures. The Tartars err from lust of pqwer ; as we iearn from 
the travels of William Rubruquis. Their mode of life is coarse 
and rude. The Pagans live by custom rather than reason, and 
suppose that their present enjoyments will be continued in a future 
life. The Idolaters resemble them in this, except that their priests 
practise chastity and abstinence. The Jews combined spiritual with 
temporal blessings ; the latter as well as the former belonging to the 
future life. The Christians, while accepting temporai wealth in the 
present life, are wholly independent of it in the future . . 867-370 

Of these sects we may place the Pagans lowest ; they are guided 
by no priesthood, and each follows his own way. The Idolaters 
have a priesthood and a ritual ; but they have a multiplicity of gods. 
The Tartars come third ; they worship one God, though with many 
superstitious and cruel observances. Next in order come the Jews, 
of whom the more spiritual attained to the knowledge of the true 
Christ. Fifth come the Christians, who practise the Jewish law 
spiritually. Finally, there is the law of Antichrist, which for a time 
overwhelms all others. And each of these has its own moral 
principle— pleasure, wealth, ambition, fame, or blessedness in a future 
life. In the mathematical section of this work it has been shown that 
there is a connexion between these sects and the various planetary 
influences, which incline men*s characters in certain directions, though 
without depriving them of free-will. As these influences change, each 
of the sects may be modified by the others. So the Saracens, though 
mainly under the influence of Venus, are modified by Jewish and 



clxviii ANALYSIS OF THE * OPUS MAJUS: 

VOL. n. PAGES 

Christian law. The TartarSi though govemed by Mars, in like 
manner are modified by Mercury, which implies Christian influence. 
The Pagans, again, and the Idolaters may differ according as the 
influence of Mars or of the Sun may prevail. With the Pagans, 
terrestial things as well as celestial may be objects of worship . 370-372 

We have now to consider the means of showing the truth of the 
Christian religion. We may appeal to miracles ; or we may take 
the ground of reason and philosophy common to us and the other 
sects. Though the Christian should not place his chief reliance on 
reason, yet he should be able to render an account of the faith that 
is in him. And as the heathen do not accept this faith, we must 
challenge them on philosophical ground. Philosophy is given to men 
for the very purpose of leading them to truth .... 372-373 

In what follows I am appealing to the wise among them rather 
than the simple. There are three kinds of knowledge : that coming 
from our own study or experience; that which is leamt 6x>m 
others, and that which is natiiral, in the sense of being shared by 
the whole species. It is no less natural to act on such truth than to 
know it« Practical and speculative reason have the same source, and 
are essentially the same, as Aristotle has taught . . . 373-375 

The existence of God is one of these natural truths, as Cicero has 
said. The neoessity of demonstrating it comes from the weakening 
effect of sin on our faculties. The divine unity is not known by 
nature; and even those who accept it are in error as to God's 
attributes. These therefore have to be explained, beginning, as the 
mathematician begins, with elementary principles. That God is an 
eternal first Cause of infinite wisdom, power, and goodness is accepted 
by the Tartars, Saracens, Jews, and Christians. Pagans cannot deny 
this tmth when presented to them; as the recent conference in 
Tartary between Christians, Saracens, and Buddhists has shown. 
Their resistance elsewhere to Christianity is due to attempts to 
impose on them a foreign yoke 375-377 

The Christian advocate may further plead that in tracing causes 
we cannot go back endlessly. There must, as Aristotle has laid 
down, be a first Cause, that has always existed, and must exist for 
ever, unchangeably. Boethius has shown that imperfection implies 
perfection, to which it is an approximation. Perlect power, as 
Aristotle shows, is boundless power : and if the power of God be 
infinite, a fortiori is His essence infinite. It follows that His good- 
ness is infinite ; and from infinite power and goodness follows the 
attribute of infinite wisdom. Such a cause is capable therefore of 
creating this world, and is disposed to govem it in the best way. 
If it be said that the world is etemal, this is to raise it to equality 
with God. If more than one Cause is asserted, then none can be 



PART VIL clxix 

VOL.II. PAGES 

infinite. In one world at least there can be only one. And if there 
should be more worlds than one, the same infinite God is capable of 
goveming them. But plurality of worlds is an hypothesis which 
Aristotle has dissipated ; for they would all tend to the same central 
point, and lose their separate existence 877-381 

God being one and infinite, man is bound to. yield Him boundless 
reverence, in thankfulness for his creation and for his hopes of future 
happiness. Even the Pagans believe in a future life; so do the 
Saracens, although their belief b tainted with thoughts of animal 
enjoyments. The Jews have the same belief. Thus the Buddhists 
have universal opinion against them. This present life is fuU of 
misery, from which we must believe that the fttture life will be free. 
In our glorified body and soul we sball participate in the divine 
nature. So too will the punishment of the evil be iafinLte. This then 
is the twofold motive for doing the will of God. But man cannot of 
himself know that will; as the difTerence of his religions show, 
differences which exist even within the pale of Christianity. Of the 
true nature even of material things we are profoundly ignorant ; 
much more of things immaterial 881-383 

Therefore Revelation is necessary. Aristotle has said that in 
these things the human mind is as the eye of the owl or bat to the 
light of the sun, or, as Avicenna says, as the deaf man to musical 
harmony, or as the untaught child to the highest tnith. Man, says 
Seneca, is too mortal for immortal things. And apart from intrinsic 
inability to discem infinite tmth he is blinded by sin. Man niust 
therefore be taught by divine authority 383-3^^5 

AII sects claim such authority. We have to consider to which of 
them has tme revelation been made. Evidently to one only, since 
God is one ; there is only one world and one human race. Avicenna 
and Alpharabius fully recognize this. We have therefore to choose 
between the six religions of which I have spoken. The Pagans and 
the Idolaters, who take creatures for God, or who assert plurality of 
gods, may be at once eliminated. When confronted by the Tartar 
emperor with Christians and Mahometans, they at once succumbed. 
The Tartars, while accepting the unity of God, worship fire, and their 
teachers are mere magicians. It is clear therefore that they are not 
in possession of the authoritative tmth which we seek. This they 
themselves have confessed. We must therefore examine the remain- 
ing three relig^ons — Jewish, Mahommedan, and Christian . 386-888 

The superiority of the Christian law is proved first by the authority 
of philosophy, which as I have before shown has given its sanction 
to the principal doctrines of Christianity. No such testimony has 
been given to Judaism or Mahommedanism. Seneca has attacked 
the Jewish creed; and Mahommedanism has been asserted by 
VOL. I. m 



clxx ANALYSIS OF THE ' OPUS MAJUS: 

VOL. II. PAGES 

Avicenna and Albumazar to be imperfect and transitory. We may 
add to this the testimony of the Sibyls. Coming more into detail, we 
find the Jewish prophets bearing testimony for Christ, and Josephus 
supplying proof that Judaism would give way to Christianity. Other 
evidence is contained in the books of Esdras and of the twelve 
Patriarchs. The authorship of these books is unknown, but they 
are of weighty authority. Further, the Jewish religion taken by itself, 
with its incessant slaughtering of cattle, is extremely repulsive ; and is 
so spoken of in the Psalms and prophetical books. Similarly the 
Koran uses very strong language in praise of Christ. Mahommedan 
writers say much in dispraise of their own sect, and admit that the 
life of its founder was stained by many vices. Accepting then the 
testimony of each sect as standing on the same level, we find none of 
them, except the Christian, testifying in favour of their own founder, 
to whom both Jewish and Mahommedan authorities, as well as 
Christian, bear witness 388-393 

The credibility of Christian writers rests on six grounds : personal 
sanctity ; wisdom ; miraculous powers ; firmness under persecution ; 
uniformity of faith ; their victory in spite of humble origin and estate. 
Besides these g^ounds for accepting Christianity, therc are the 
miracles wrought by Jesus, especially the forgiveness of sins, the 
surest proof of His Divine nature. For neither Moses nor for 
Mahomet was divinity claimed. There is the yet further proof of 
holiness of life, which both in Mahommedanism and Judaism is 
found wanting. In neither is there any recommendation of poverty, 
chastity, and obedience. Nor is the sanction of a future life clearly 
sct forth in them 393-396 

Having thus proved that the Christian faith is to be accepted as 
true, we need not examine each one of its articles. There is however 
one of them as to which much difficulty has been experienced, the 
Sacrament of the Altar. I wish therefore to give reasons why it 
should be willingly and ardently accepted, containing as it does the 
essence of the whole. First, it is accepted by the whole Christian 
Church. Secondly, it is manifestly set forth in Scripture, as in the 
Gospel of St. John, and in the Book of Wisdom, and in the Epistle of 
St. Peter. Thirdly, it is confirmed by the unanimous authority of the 
saints. Fourthly, we may add the testimony of innumerable miracles, 
of which I here record two of undoubted authenticity and recent date. 
Finally, as the Creator is omnipresent throughout the world, so by 
this sacrament is the Hedeemer omnipresent to those who are in 
a state of grace. Without the Creator*s presence the creature would 
cease to exist. So without the Re-creator*s presence would the 
re-created fall from the state of g^ce. It consists with the infinite 
power and goodness of Christ that this infinite good should be 



PART VII. clxxi 

VOL.II. PAGES 

shared by those who have been re-created. This sacrament is a con- 
tinual renewal of the sacrifice by which Christ has taken away the 
sins of the world. He who made the original sacriiice will be willing 

torenewit 396-400 

But it is not enough for reason to be convinced in this matter ; it 
is necessary that the heart be stirred. We must feel that this sacra- 
ment' contains in itself the highest good, the union of man with 
God. We must feel that in every Church, for each recipient who 
is in the state of grace, in every part of the Sacred Host, the whole 
Deity is contained. Thus humanity transcends itself, and ceases to 
be bound within the limits of space and time. To the priest is 
given in this Sacrament a far greater power than that of creating 
a universe. The utterance of five words brings the Creator into 
communion with us. Again, what would be impossible to sense, to 
sustain the presence of God, is thus rendered possible. St. Dionysius 
was not abie to endure the sight even of the Holy Virgin. How 
then could we endure the Divine presence? £ven under the veil. 
of this sacrament the heart is overwhelmed. Only when thus veiled 
would it be possible for us to eat of Christ's flesh and drink His 
blood. We are thus prepared to believe that all our truest blessings 
lie in a world beyond the world of sense. We are thus made one 
with God and Christ ; and to what greater good than this can man 
aspire? 400-404 



ixi a 



ANALYSIS OF 
'THE MULTIPLICATION OF SPECIES/ 



PART I. 

CHAPTER I. 

VOL. II. PAGES 

(a) As to the name and the essential meaning of species. 

By species is here meant the first eifect of any natural agent. Thus 
light passing through space is the species of the light in the sun. 
If light passes through coloured glass, the colour shed by the light 
is called the species of the originating colour. Species is here used 
in the sense of likencss or image. In a dream the hallucination is 
a species. Intention, form, virtue, impression, passion, are other 
words uscd to express it 407 410 

This first effect of the agent resembles the agent. The agent 
transmutes the patient into its likeness ; thus fire transmutes what it 
acts on into fire, heat into heat, light into light, and so on. The 
subsequent effects have not the same likeness to the agent. This 
first effect is of the same specific nature as the agent, otherwise we 
should be at a k>ss to assign its category ; for it cannot belong to the 
category of accidents; and there is nothing intermediate between 
subsUnce and accident. But, although of the same nature, its 
essence is incomplete ; just as we should say of the embryo, only 
that the incompleteness is far greater. Some agents produce more 
complete species than others, as light, colour, heat Generally 
speaking, the higher tbe rank of agents, the more incomplete are 
theirspecies 410-413 

{6) There can be only one such resembling effect f<M- each agent. 
This we call univocal ; the multiple secondary effects may be called 
equivocaL While the agent is acting on the patient, the effect or 
virtue is called species ; afterwards, when the eifect b completed, it 
takes the name of the agent. Fire, when it has taken hold of the 



clxxiv ANALYSIS: MULTIPLICATION OF SPECIES. 

VOL. II. PAGES 

wood, is called fire. This, however, is only true when the patient is 
comiptible ; when the patient is incorruptible, the case is otherwise. 
The sun does not communicate its nature to the moon and planets 
by shining on them. The species of light is completed in them, but 
not the species of the sun. And generally it would be truer to say 
that the patient was assimilated through the species to the nature of 
the agent, than to speak of the patient losing its identity in that 

oftheagent 413-416 

(c) Natural agents produce the same species whatever be the 
nature of the patient ; in other words, their action is uniform. This 
does not apply to agents possessing free-wili, except in so far as they 
may resemble natural agents. The diiference in the patient may 
bring about a difTerent result, but the species is the same . . 417-418 

CHAPTER II. 

(a) We have now to inquire what are the things which generate 
species. First, all qualities that act on sense, producing some change 
in the sense-organ. There may be a doubt as to sound. Here 
there is a tremor in the part of the object struck : this tremor is com- 
municated to the adjacent part, and so again to the next. The first 
tremor makes a sound ; so does the seoond and the third; but the 
second sound does not come from the first sound ; it comes from its 
own tremor 418-419 

(b) Do substances generate species ? Assuredly, since substances 
are nobler than accidents. An accident is not generated until its 
subject be first generated. Heat, the accident, is posterior to fire, 
the substance. When heat appears in watcr, fire must pre-exist, and 
the substantiai nature of fire, and this we call the species of the 
substance fire. Such species are not cognizable by the five senses, or 
by sensus communis. But they are cognizable by a mental process, 
akin to that which causes the sheep instinctively to flee from the wolf 
which it has never before seen, feeling something injurious in its 
proximity. It is sometimes said that substance can have no contrary : 
but there is a sense in which substances, or substantial forms act in 
opposition 419-428 

(c) The species of substance is of the whole compound ; i. e. of 
matter and form, not of form alone 428-424 

(d) Every corporeal substance can produce species, therefore also 
the organs of sense. The species generated by the organs of sense 
are concemed in sensation 424-425 

(e) With regard to matter, which is passive, it may be affirmed 
that it does not generate species, except in so far as compounded with 
form 425-427 

(/) Light and colour generate species, but other properties of body, 



PART L dxxv 

VOL, II. PAGES 

such as magnitude, position, motion, &c., which are apprehended 
by sensus communis^ do not. The magnitude and figure of an object 
are inferred from the species of light and colour that issue from it ; not 
by species of magnitude and figure. Stili more obviously is this the 
case with properties iike proportion, relation, and position . 427-430 

(g) Of things some are universals, some are particulars ; species 
issue from both. Universals do.not exist apart finom their particulars, 
neither do their species.. The species in every case is of the same 
nature as the source from which it issues 430 431 



CHAPTER III. 

\Ve have considered the agent ; we are now to. consider the mode 
of action. It is not correct to say that the species is something 
which issues from or is emitted by the agent. Nor is it created out 
of nothing. Nor again is it an impression made upon the patient as 
with a seal upon wax. The true view is that the species results from 
a change in the potential activity of the recipient matter. We must 
distinguish between the potentia aciiva and the potenHa receptiva, 
The laitter is that on which the Creator impiants Form. But it is the 
potentia activa which is here in question. The agent produces its 
eflfect, not by union of its substance with the patient, but by stimulating 
the latent activity of the matter which is acted on . • . 431-434 

Action does not take place at a distance. Force is not exerted by 
the agent except on the part of the patient with which it is in immediate 
contact. The efTect generated in the first part of the patient becomes 
a force acting on the second, and so onward. Action is thus propa- ' 
gated from particle to particle 434-436 

It is objected to this view that a ray of light passing through 
coloured glass produces bright colours on an opaque screen; how 
could such colours be evolved from the potential activity of the 
intervening air, a simple substance ? The reply is that the species 
produced in the air is extremely feeble. It only becomes relatively 
strong on reaching the screen which is so constituted as to develop 
colour. In the same way the species of the magnet is feeble until it 
reaches the iron which is better adapted to receive it. The colour on 
the opaque screen is but the species of colour, and is £ar from being 
so complete as it appears 436-438 



CHAPTER IV. 

Six propositions have now to be considered. {a) It is not possible 
to assign a minimum of quantity below which a given agent will cease 
to act. In animate agents there b an augmentative power bringing 



clxxvi ANALYSIS: MULTIPLICATION OF SPECIES. 

VOL. II. PAGKS 

the agent up to a given d^ee of force. In inanimate agents the force 
is simply proportionate to the quantity, however small the quantity 
may be. It may be so small as not to be appreciable by the senses, 
and yet none the Jess act, For instance, the smallest particle of 
matter, all appearances to the contrary notwithstanding, possesses 
gravity 438-441 

(b) Thc whole agent acts along the whole line of its depth on the 
patient ; not merely that extremity of the agent which comes into con- 
tact with the patient 441-442 

(c) A certain definite portion of the patient is affected by the agent, 
and no more. The sun and the moon diifuse light through similar 
dimensions of the medium, although with enormous differences of 
intensity, corresponding to their differences of magnitude . • 442-448 

(d) Will less than that definite portion suffice for the action ? It 
will not, unless that lesser portion be disunited from the rest, so as 

to become a whole in itself 443 

(e) Does half of the agent act on half of the portion affected, or does 
the whole act on the whole portion ? The whole acts on the whole 
portion 443-444 

(/) Does the half of this portion first aflfected, carry on the chaiige 
to the second half, or does the whole change come from the agent ? 
The latter is the true view 444-445 

CHAPTER V. 

(a) With regard to the patient, how can terrene substance be 
acted on by celestial, which is of different kind, since celestial is 
incorruptible ? The reply is that whatever the difference between 
celestial and terrestrial substance, yet the species generated by the 
former are communicable to the latter 445-446 

{b) One celestial body may act on another ; not by changing its 
specific nature, but by bringing that nature to greater per- 
fection 446-447 

(c) We must admit that, in a certain sense, terrene things act on 
cclestial, since there is a sense in which all parts of the universe are 
assimilable to all the rest. In vision species pass from the eye to the 
object seen. Such species do not change the specific nature of the 
celestial object, nor interfere with its superiority ; they do but draw 
out that which it has in common with the lower . . . 447-449 

CHAPTER VI. 

We have, lastly, to consider what corporal agents are capable of 
completing their action on patients affected by them. (The earth, as 
the central point of the universe is the great region of change. The 



PART II. clxxvii 

VOL. II. PAGES 

heavenly bodies moved by spiritoal intenigences are unchangeable.) 
We shall find that the four elemental substances can carry their 
action to completion, and especially the element of fire . . 449-451 

But many compound substances are higher in rank than the 
elemental. Why cannot they do the same ? There resides in them 
an aptitude for doing this, but they are practically debarred from 
doing it. Were it otherwise, the higher substances would transmute 
the lower into their own substance, and the lower would disappear, 
and thus the order of the universe would be snbverted. Consequently 
spiritual and celestial substances, while generating their species, 
cannot bring them to actual completion. Such compound substances 
as the heavens or as man, if their species were made complete, would 
do away with all lower substances. Consequently, the carrying of 
species to their complete effect is limited to very few substances, such 
as the elements, and especially the element of fire . . • 451-455 

The same thing is to be said of attributes or accidents. Some of 
these, as hot, cold, moist, dry, can complete their species, especially 
the accident of heat. Light also can do this in bodies adapted to it. 
Of colour, odour, savour, and sound tbe same cannot be said . 455 456 



PART II. 

CHAPTER I. 
We now have to consider the mode in which the radiation of 
species takes place. The first part of the patient, when acted on, 
becomes itself a force acting upon the second part, and so onward. 
These successive parts of the patient are of equal dimension. From 
the starting-point in the agent, or, which is the same thing, from the 
point of the patient first affected, emanate rays in all directions in 
straight lines. Those emanations, of whatever kind they be, are 
called raysy by analogy with what we see emanating from a star 
or any luminous point. Their rectilinear direction continues until 
modified by an opaque sur&ce which reflects them, or a change of 
medium which refracts them. These lines are not merely of one 
dimension : they have breadth, and depth, as well as length . 457-460 

CHAPTER II. 
There are five kinds of rays to be considered. (a) Rectilinear 
rays, where the medium is uniform. (d) Refracted rays. The ray 
passing from a rarer to a denser medium is deflected towards the 
perpendicular drawn to the surface at that point ; and conversely, 
when passing from deaser to raier. (c) Reflected rays. When the 



L 



clxxviii ANALYSIS: MULTIPLICATION OF SPECIES. 

VOL. II. PAGKS 

ray meets an opaque surface, it is tumed back in a direction making 
with the perpendicular to the surface an angle equal to the angle of 
incidence. {d) In the case of animate bodies, the ray follows 
a tortuous path along* a nerve towards the centre of sensation. (e) 
Secondary, or aocidental, rays may be emitted, not from the luminous 
point, but from the principal ray : as in the case of rays coming 
through an opening into a dark room, from which secondary rays 
are dispersed through the room ; although the eye placed in one 
of those rays cannot see the luminous point. Rays from the sun 
of this kind are of greater utility to living beings than direct 
rays 460-465 

CHAPTER III. 

Whether the ray falls on a line or on a surface, whether the sur- 
face be plane, convex or concave, the law is the same. The mode 
of measuring the incident and the reflected angle is explained else- 
where. In refraction from the rarer to the denser medium the ray 
is deflected towards the normaL From the denser to the rarer 
away from the normal. The accompanying diagrams will illustrate 
this. Perpendicular rays, coinciding with the normal, are not 
deflected 465-468 

What is the cause of reflexion and refraction ? All media, however 
transparent, offer a certain amount of resistance to the passage of the 
ray. This is more completely overcomc by the perpendicular than 
by the oblique ray. The oblique ray, passing into the denser 
medium, follows the course of the perpendicular ray as far as 
possible, i. e. is deflected towards it, as being the path of least 
resistance. On the contrary, when passing into the rarer medium, 
the energy which it has been hitherto exerting in the denser, now 
finds a vent in carrying it away from the normal, i. e. along a path 
of greater resistance 468 470 

That these are the respective paths followed, is shown by the 
double refraction taking place when rays impinge on a globular body 
filled with the denser medium. The diagram shows that the rays 
issuing from the globe converge to a point, and that at this point 
combustible substances arc ignited . . . . . . 470-472 

CHAPTER IV. 

To what extent does refraction take place in thc heavens ? The 
celestial orbs are of the same degree of translucency ; in these there- 
fore there is no refraction of rays. Rays passing from the sphere of 
ether to that of air (which latter includes that of fire) are refracted ; 
since ether is the more subtle medium. The proof of this is that the 



PART IL clxxix 

VOL. II. PAGES 

apparent polar distance of a star is less when rising than when passing 
the meridian. At the zenith, the ray, impinging on the sphere of air 
perpendicularly, is unrefracted* At the horizon it is refracted. With 
the circumpolar stars the polar distance appears less, when they pass 
the meridian nearer the horizon, than when they pass it nearer the 
zenith ; for the same reason. The precise quantity of this refraction 
can be measured by astronomical instruments. Ptolemy first indicated 
this source of enror, and Alhazen has verified it. It has to be taken 
account of in lunar tables 472-476 

There is no subsequent refraction between the sphere of fire and i 
that of air, as the one passes into the other by imperceptible 
degrees 476-477 

Rays falUng from the planets on regions of the earth beyond the 
tropics must all fall obliquely and therefore be refracted • . 477-478 

CHAPTER V. 

(a) No bodies are so dense that rays may not pass through them, 
though these may not always be perceptible by human organs. Some 
bodies of intermediate density may partly refract, and partly reflect 
the rays, as in the case of water 478-479 

{b) Hardness and solidity are to be distinguished from density. 
Glass and crystal, though hard, must yet be rare, i.e. their partides 
must lie somewhat far apart, since rays pass freely through them. 
Hardness depends not on the number of the particles but on stability 
and freedom from moisture. (^) Reflexion depends on the smooth- 
ness of the surface that reflects. A rough surface disperses the rays 
in difierent directions 479 

(d) We must not suppose that the ray produces any effect on the 
surface that reflects it. No secondary or accidental ray is generated at 
the point of reflexion. Were it so, such an efTect would be visible, 
whatever our position might be with regard to the mirror. AII that 
the reflecting surface does is to change the direction of the ray. 
The reflected ray.is strictly continuous with the incident ray . 479-481 

CHAPTER VI. 
In reflexion, the angles made by the incident and the reflected ray 
with the perpendicular to the surface are equal. This may be shown 
experimentally by an instrument constructed for the purpose, and 
the diagrams annexed give geometrical proof of it. The rule holds, 
whether the reflecting surface be plane, concave, or convex . 481-486 

CHAPTER VII. 
Rays reflected from a plain surlace are diveigent. Rays reflected 
from a spherical concave surface converge at various points on 



clxxx ANALYSIS: MULTIPLICATION OF SPECIES, 

VOL. 11. PAGES 

the diameter which forms the axis of the mirror; those from the 
circumference of any circle drawn on the mirror in a plane perpen- 
dicular to the axis will meet in a point. The smaller the cirde the 
greater wiil be the distance of the point of convergence from che 
mirror ; and conversely. (Such circks are, of course, merely 
imaginary ; they merely indicate a series of points similarly placed 

with regard to the axis) 486-490 

But another form of concave mirror has been devised in which the 
curvature is such that all the rays shall converge to a single point. 
}*his cannot be explained here, but it may be mentioned that the 
curvature is that of a conic section 490-491 

CHAPTER VIII. 
Rays from the object proceed equally in all directions, as radii 
from the centre of a sphere. It is objected thatrays passing through 
an angular orifice illuminate an angular not a circular space. But 
this depends on the distance of the illuminated surface from the 
orifice. If the distance be sufficient, the illuminated surface is cir- 
cular. The smaller the orifice, the less the distance required to 
obtain this result. Much depends also on the strength of the rays ; 
those of the sun at noonday, being stronger, produce the result more 
readily than the feebler rays of moming Hght. For the same reason, 
at noon a smaller portion of the solar surface will effect the result than 
in the moming ; in the latter case the illumination not being circular, 
much will be dispersed and lost. That the shape of a flame is not 
spherical but conical, is due to the ascending force of the particles. 
In the sphere of fire, where there is no :such force, the fire assumes its 
natural (spherical) shape. The centre of the illuminated surface is 
most strongly illuminated ; the surrounding parts being illuminated 
by intersecting rays, and therefore more feebly. Since all regular 
figures can be inscribed in a circle, the spherical fomi of emission of 
rays includes all the others, and especially the conical . . 491-494 

CHAPTER IX. 

Species proceed from every point in the agent, not from one only. 
We see this in the case of shadows. If an illuminated body be less 
than the illuminating, the shadow formed is conical and limited ; if 
the two are equal, it is cylindrical and unlimited. If the illuminated 
body be greater, the shadow is divergent and unlimited. We are 
supposing that the agent is homogeneous. If it be heterogeneous, 
we must consider each homogeneous part separately. In dealing 
witb the cone of rays proceeding from any point, we have to remember 
that it is the axis of the cone, directed vertically to the surface acted 



PART IIL clxxxi 

VOL. II. PAGES 

on, wfaich is specially potent, and has the greatest penetrative power. 
It is to be noted that rays prooeeding from a very distant source 
appear parallel, though in reality they are not so : so the walls of 
a house seem parallel to each other, though in reality each is directed 
to the centre of the earth 494-498 

CHAPTER X. 

Optical principles teach us that in looking at a sphere the visual 
cone embraces less than half the surface. In considering the portion 
of a convex or concave surface that can be illuminated by a source of 
light, we have to determine to what portion of it rectilinear rays can 
proceed from the illuminating point without impediment. In the 
mutual action of two spheres, more than half the surface of the smaller 
is involved, less than half of the larger 498-501 



PART III. 

CHAPTER L 

We have now to consider the natiire of species as existing in the 
medium. Many have regarded it as body. But this is misleading. 
To speak of it as body would imply that it was something which 
divided the surrounding medium, having three dimensions of its own. 
But the species has no dimensions other than those of the medium in 
which it is generated. During the generation of species from the 
medium, the medium does not lose its corporeal character, nor is any 
new body created or added. The species is simply a portion of the 
medium wrought on in a peculiar way by the agent. Though so 
wrought on as to resemble the agent, yet the substance of which it is 
formed is that of the medium 502-504 

But the species moves onward in space, while the medium remains 
at rest : how can the species be said to have the bodily substance of 
the medium ? The reply is that the species successively formed are 
not numerically identical. What takes place is the successive genera- 
tion from point to point of something new, as in the case of a shadow 
apparently shifting its position, but which is really being constantly 
renewed. It is asked why does not the movement of the air by wind 
affect the direction of the specles? The reply is that the force 
exerted by the agent is in a definite direclion and renews the species 
in each pwrtion of air as it is driven by. In the case, again, of reflex- 
ion, there is no violent casting back of the species : it simply pursues 
the only path possible to it What we call species is not one identical 



clxxxii ANALYSIS: MULTIPLICATION OF SPECIES. 

VOL.II. PAGES 

thing, but a continuous succession, each generating that which foUows. 
It has been said that light is body, or an emanation from body. But 
Aristotle denies this, remarking that in that case we should perceive 
its translation from east to west at sunrise. The remarks on the 
subject in the Topics are not to be taken as conveying Aristotle's 
real opinion 504-507 • 

CHAPTER II. 

The second question is whether the species of a corporeal agent 
should be regarded as corporeal or spiritual. Clearly the former: 
since it is not a soul, or an intelligence, or a first cause ; and these 
only can be considered as spiritual. The species must be of like 
nature with the agent, and of like nature with the completed eifect. 
It canpot be of nobler nature than that which generates it. Some hold 
that, though in its essence corporeal, yet its inode of existence is 
spiritual. But there cannot be this disparateness between the essence 
and the mode of existence. The essence of the species has dimension, 
derived as we have seen from the medium ; it is therefore corporeal. 
It is said that it has not material essence (material being here taken 
for corporeal). But even spiritual substances have material essence : 
they are compounded of form and of matter: much more, there- 
fore, are species material. It has' been already shown that the 
species of corporeal substance re^mbles the total compound. In 
the medium not merely is the formal essence generated but the 
material, although the essence be incomplete. I therefore conclude 
that the species of a corporeal object is corporeal . . . 507-509 

The contrary view has arisen from imperfect translations of Aver- 
roes, Avicenna, and Aristotle. In these the word insensible has been 
mistaken for immaterial. And because spiritual things are insensible, 
therefore what is insensible has been taken to mean spiritual and 
immaterial. It is objected that species are not always insensible, as 
when a ray passes through a window or through coloured glass. But 
this is only accidental. Some expressions of Avicenna as to the 
reception of impressions in the brain have been wrongly interpreted. 
They must be taken in connexion with what Aristotle has said on the 
same subject 509-511 

CHAPTER III. 

I pass to the question of the mingling of species in the medium. 
The question is one of much difficulty, but Ptolemy and Alhazen 
throw great light upon it Species of the same kind melt into one, 
and if opposite, then the stronger overwhelms the weaker. Those 
that are contingent, i.e. have no relation to each other, co-exist 



PART IV. clxxxiii 

VOL. II. PAGES 

separately. Species in fact act in this respect as do their agents, 
and as do their completed eflects. Alhazen thus explains the unity 
of impression resulting from species of an object entering the two 
eyes ; they are united in the brain. But if species are thus mixed, 
how do we recognize various objects as distinct ? Because through 
the point of mixture some rays come perpendicularly from the object 
to the eye, others come to this point obliquely; these latter are 
edipsed by the former. We may remark further that the various 
parts of the agent are always active : the generation of the species 
is therefore continuous. Species unrelated to one another do not 
commingle ; they exist separately and simuhaneously . . 511-516 



PART IV. 

CHAPTER I. 

We have now to consider how and why species are weakened in 
their transit. Is ihere resistance in the medium ? There is. For 
every agent produces rarefaction and condensation, as the first process 
in every natural action. What is rare resists condensation, and con- 
versely. Therefore every medium offers resistance. Further, there 
is a practical limit to rarefaction. It may be said that resistance is 
only ofTered by contraries, and that, to many agents generating 
species, nothing is contrary, in the sense in which darkness is contrary 
to light. But the resistance is not to the species themselves, but 
to the processes of rarefaction or condensation which accoropany 
them 517-518 

It is obvious that species, so long as they continue to radiate, and 
are not arrested by an accumulation of such material as will intensify 
their action (as in the case of fire acting on fuel), are weakened by 
distance. The senses are less afTected by a distant than a near 
object. Two causes may be assigned. It is said to be a law that, 
as the first species is weaker than the agent, so the second is weaker 
than the first, and so on. This, however, is not invariable. If iron 
be held at some distance from a magnet, the iron is more affected 
than the air between them. So a ray, passing through coloured glass, 
produces a stronger effect on a distant wall than on the intermediate 
air. Another reason may be assigned. The agent radiates force in 
all directions. Much force is dispersed thus. And though, for special 
reasons, the force in any one line may be found not to grow weaker, 
yet it will be so where the medium is ordinarily pervious. Thus both 
distance and radiant dispersion account for the weakening of species. 



dxxxiv ANALYSIS: MULTIPLICATION OF SPECIES. 

VOL. II. PAGES 

When the direction of radiation is from terrestrial to celestial, it 
might be thought that the increasing rarity of the medium would 
compensate the weakening of the species from dispersion ; but the 
second cause operates at a faster rate than the first. For radiation 
in the reverse direction, from heaven to earth, there can, of course, be 
no such compensation 518-521 

CHAPTER II. 

Supposing space were unlimited, could multiplication of species go 
on indefinitely ? No ; for, as we have seen, the species grows con- 
tinually weaker the further it is from its source. If the supply of 
matter on which it could operate were infinite, then no doubt the 
action would be infinite ; but this is not the case. It might be said 
that, since matter is infinitely divisible, there would always remain 
something on which the species, however enfeebled by distance, 
could act; that therefore the duration of the action would be infinite. 
But this seems a forced and unsatisfactory conclusion. Again, it 
might be urged that the medium may grow continually more subtle so 
as to correspond to the continual weakening of the species. But this 
does not in fact take place. As a fact, the resistance, in our world, 
which is finite, is always sufficient to prevent the species from 
passing beyond a certain distance 521-524 

Supposing the existence of a vacuum between earth and heaven, 
no species could radiate ; for no natural action can take place in 
a vacuum. It follows also that beyond the ninth and tenth heavens 
no species from the stars can radiate. For beyond these there is 
nothing, not even empty space 524-525 

CHAPTER III. 

The radiation of force takes place in time. For it involves change 
in the medium; and change involves time. When the path of 
propagation is refracted, more time is taken than when the path is 
direct. Finite force cannot act instantaneously, for then it would be 
equal to infinite force. As a point is to an instant, so is a line to 
time. The passage of a point is instantaneous, in the passage of a line 
time is occupied. Translation implies before and after • . 525-526 

•It is said that the transit of light is instantaneous. But all that is 
meant is that the time required is insensible. Aristotle, in saying 
this, is arguing against Empedocles, who regarded light as a substance 
flowing from the luminous body. In this case no doubt we should be 
able to see its passage from east to west in the heavens. But the 
view here taken of light is not that it is a body translated, but 
a movement contbuously propagated. Aristotle no doubt dis- 



PART V. clxxxv 

VOL. II. PAGES 

tinguishes the propagation of light from that of sounds or odours. 
But the distinction is of degree ; light being more subtle, its motion 
is more rapid 526-528 

Alkindi urges that, though through short distances the transit of 
light may be imperceptible to our senses, yet that the summation of 
short periods would amount, in the transit from east to west, to some- 
thing that would be perceptible. But of imperceptibility there are 
many d^ees ; and the propagation of light is so rapid that the 
summation of a vast number of imperceptible periods may still not 
reach the point at which perception of time by human sense is 
possibie 528 

1 1 is further maintained that in radiation of species, as here described, 
more time would be occupied than in translation of a body through 
space : because between the formation of any one species and the 
formation of that which foUows it, there is an interval of rest. The 
fact is, however, that the resistance of the medium to a body carried 
through it would be far greater than it would be to the formation 
of species, which involves an exceedingly slight disturbance of the 
medium ; so that the motion in this iatter case will be far more rapid, 
and the interposition of intervals of rest wiil pass unperceived . 528-529 



PART V. 

CHAPTER I. 
In propagation of species we have to consider, first, tbat which we 
call univocaly as when ligbt makes light ; secondly, the equivocal, as 
when iight makes heat, or any other effect of a different kind. As to 
the first, we remark that the strongest are those which proceed by 
direct lines, as contrasted with those which are refracted or reflected. 
We may omit for the present those which proceed on tortuous paths, 
as in the case of nervous action ; since here a difierent agency, that 
of life, comes into play. The species called accidental, i. e. which 
proceed, not directly from the object, but secondarily from the species, 
arethefeeblestofall 530-534 

CHAPTER II. 

The path of some species falls perpendicularly on the object ; these 
are the strongest ; and this whether the object be a plane surface or 
curved. In either case the angles made are equal. That which 
impinges on the convex surface of a sphere, is stronger than that 
which falls on the concave surface, as being necessarily shorter. The 

VOL. I. n 



clxxxvi ANALYSIS: MULTIPLICATION OF SPECIES. 

VOL. II. PAGES 

refracted ray is stronger than the reflected, its path lying nearer to 
the direct perpendicular ray. The ray refracted by passage frorn 
a denser to a rarer mediiun is less potent, for the same reason, than 
the ray refracted from rarer to denser. In the case of reflected rays, 
those that make an angle with the vertical line produce a greater 
effect than those that fall vertically ; not merely because they divcrge 
less from the direct ray, but because they can be accumulated by 
suitably shaped mirrors. Some of these are described, though 
I have not myself seen them, which bringrays to a focus both in front 
and behind them 534-539 

CHAPTER III. 
Cones of rays come from the agent to each part of the surface 
acted on. The shorter the cone, the stronger is the action. The 
shortest cone is thus defined. Let a circle be drawn in the agent 
sphere dividing its operative from its inoperative part. From any 
points in the circumference of this circle let diameters of the sphere 
be drawn. Tangents to the sphere at the extremities of these 
diameters wiil form the shortest cone. Other points connected 
with this subject are illustrated by the accompanying diagrams . 539-548 



PART VI. 

CHAPTER I. 
As species are generable, so are they corruptible. And this 
in two ways: (i) from exhaustion of their own strength; (2) from 
tendency in the substance acted on to resort to its own natural 
condition , . 544-545 

CHAPTER II. 
When the generating agent is removed, does the species at once 
disappear ? Not instantaneously, but gradually, from the causes stated 
in the previous chapter. The apparent permanence in some cases of 
the species, after the agent has disappeared, is to be explained. The 
semen retains its force in the absence of the male parent ; but here 
the female supplies the place. A heated stone retains its heat. Here 
the species, i. e. incomplete effect, has passed into a more complete 
eifect 545-547 

CHAPTER III. 
Are thereiterated actions of the agent on thepatient to be regarded 
as niunerically idendcal, or as distinct ? They must be regarded as 



PART VL clxxxvii 

VOL. II. pa<;es 
distinct. Therc is no qucstion here of anything being created. The 
action and motion are not fixed and permanent things, but successory. 
If a box be made and then taken to pieces, and subsequently put 
together again, we consider that it has been twice made, although 
out of the same material 547-549 

CHAPTER IV. 

In a transparent medium, does the first species continue during 
the presence of the agent, or is it destroyed and renewed? The 
latter is the case. There is far more rapid dispersion in a rare than 
in a dense medium. In certain regions, as inthe tropical zone where 
the sun is vertical for a considerable time, there is less rapid and 
complete dispersion. Much depends on the nature of the body 
acted on. Dense bodies retain the effect for a longer time than rare. 
The foregoing remarks apply to terrestrial and corporeal things. 
They would need qualification if applied to things spiritual or things 
celestial 549-552 



FRATRIS ROGERI BACON 

ORDINIS MINORUM, OPUS MAJUS. 



PARS PRIMA 

HUJUS PERSUASIONIS, 

IN qua excluduntur quatuor universales causae totius igno- 
rantiae humanae, habens quatuor distinctiones. In prima sunt 
quatuor capitula. In primo data totius persuasionis intentione 
reprobantur illae quatuor causae universali sermone. 

Capitulum L 

Sapientiae perfecta consideratio consistit in duobus, vide- Definition 
licet, ut videatur quid ad eam requiritur, quatenus optime ^ ^* ^'"* 
sciatur ; deinde quomodo ad omnia comparetur, ut per eam 
modis congruis dirigantur. Nam per lumen sapientiae ordi- 
natur Ecclesia Dei, Respublica fidelium disponitur, infidelium 
conversio procuratur; et illi, qui in malitia obstinati sunt, 
valent per virtutem sapientiae reprimi, ut melius a finibus 
Ecclesiae longius pellantur quam per effusionem sanguinis 
Christiani. Omnia vero quae indigent regimine sapientiae 
ad haec quatuor reducuntur; nec pluribus potest comparari. 
De hac igitur sapientia tam relate quam absolute scienda 
nunc, secundum tenorem epistolae^, quicquid possim circa 

' Epistolae praecedentis, Cottonian MSS., JuL D. v. (hereafter referred to as 
Jul.\ Thts was the letter of Pope Clement IV. It ran thus : 

* Dilecto filio Fratri Rogerio dicto Baccon ordinis Fratnim Minorum. 

* Tuae devotionis literas gratanter recepimus, sed et verba notavimus diligenter 
VOL. I. B 



2 OPERIS MAJORIS PARS PRIMA. 

persuasionem ad praesens Vestrae Beatitudini praesentare 
conabor. Quoniam autem illa, de quibus agitur, sunt grandia 
ct insolita, gratiam et favorem humanae fragilitatis requirunt. 
Nam secundum Philosophum septimo Metaphysicae, ea quae 
sunt maximae cognitionis secundum se, sunt minimae appre- 
hensionis quoad nos. Involuta enim veritas in alto latet et in 
profundo posita est, ut dicit Seneca septimo de beneficiis, 
et quarto Naturah*um. Et Marcus Tullius in Hortensio dicit, 
quod omnis noster intellectus multis obstruitur difficultatibus, 
quoniam ipse se habet ad manifestissimum in sua natura, sicut 
oculus noctuae et vespertilionis ad lucem solis, ut Philosophus 
dicit secundo Metaphysicae, et velut surdus a nativitate ad 
dclectationem harmonicam, sicut undecimo Metaphysicae dicit 
Avicenna. Quapropter sufficit nobis in inquisitione veritatis 
proprii iotellectus imbecillitas, ut quantum possumus causas 
et occasiones erroris extraneas longius a debilitate sensus 
nostri relegemus. 
Kourcauscs Quatuor vcro sunt maxima comprehendendae veritatis 
authority, offendicula, quae omnem quemcumque sapientem impediunt, 
custom, et vix aliquem permittunt ad verum titulum sapientiae 
j^^udke, pervenire, videlicet fragilis et indignae auctoritatis exem- 
presump- plum, consuetudinis diuturnitas, vulgi sensus imperiti, et 
knowlcdge. propriae ignorantiae occultatio cum ostentatione sapientiae 
apparentis. His omnis homo involvitur, omnis status occu- 
patur. Nam quilibet in singulis artibus vitae et studii et 
omnis negotii tribus pessimis ad eandem conclusionem utitur 
argumentis, scilicet, hoc exemplificatum est per majores, 
hoc consuetum est, hoc vulgatum cst ; ergo tenendum. Sed 
oppositum conclusionis longe melius sequitur ex praemissis, 
sicut per auctoritatem et experientiam et rationem multi- 

quae ad explanationem eanim dilectus filius G. dictus Bonecor miles viva voce 
nobis proposuit tam fideliter quam pnidenter. Sane ut mdius nobis liqucat 
qutd intendas volumus et tibi pcr Apostolica scripta praecipiendo mandamus 
quatenus, non obstante praecepto praclati cujuscunque contrario vel tui ordinis 
constitutione quacunque, opos illud quod te dilecto filio Raymundo de Lauduno 
communicare rogavimus in minore officio constituti scriptum de bona litera 
nobis mittere quam dtius poCeris non omittas, et per tnas nobis dedares literas 
quae tibi videnter adhibenda esae remedia drca ilU quae noper esse tanti 
discriminis intimasti, et boc quanto secretius poteris hudm indilate. Datum 
Viterbii x Kalend Julii anno ii.' (^Wadding, A mmmits Mimo § »um^ voL hr, p. 265.) 



CAUSAE ERRORIS. 3 

pliciter • probabo. Si vero haec tria refellantur aliquando 
magnifica rationis potentia, quartum semper in promptu est 
et in ore cujuslibet, ut quilibet suam ignorantiam excuset ; et 
licet nihil dignum sciat, illud tamen magnificet imprudenter, 
ut sic saltem suae stultitiae infelici solatio veritatem opprimat 
et elidat. Ex his autem pestibus mortiferis accidunt omnia 
mala humano generi; nam ignorantur utilissima et maxima 
et pulcherrima sapientiae documenta, et omnium scientiarum 
et artium secreta ; sed pejus est, quod homines horum quatuor 
caligine excaecati non percipiunt suam ignorantiam, sed cum 
omni cautela palliant et defendunt, quatenus remedium non 
inveniant ; et quod pessimum est, cum sint in tenebris errorum 
densissimis, aestimant se esse in plena luce veritatis ; propter 
quod verissima reputant esse in fine falsitatis, optima nullius 
valoris, maxima nec pondus nec pretium obtinere et e con- 
trario falsissima celebrant, pessima laudant, extollunt vilissima, 
caecutientes,aliud esse omnem sapientiae fuIgorem,fastidientes^ 
quae magna facilitate possunt adipisci. Et propter stultitiae 
magnitudinem ponunt summos labores, consumunt tempora 
multa, magnas expensas effundunt in iis, quae nuUius utilitatis 
vel parvae sunt, nec dignitatis alicujus secundum judicium 
sapientis. Et ideo necesse est ut violentia et malitia harum 
quatuor causarum omnis mali cognoscantur in principio, et 
reprobentur, et longe a consideratione sapientiae relegentur. 
Nam ubi haec tria dominantur, nulla ratio movet, nullum jus 
judicat, nulla lex ligat, fas locum non habet, naturae dictamen 
perit, facies rerum mutatur, ordo confunditur, praevalet vitium, 
virtus extinguitur, falsitas regnat, veritas exsufflatur. Et 
ideo nihil magis necessarium est considerationi, quam certa 
damnatio istorum quatuor per sententias sapientum electas, 
quibus non poterit contradici. 

Quoniam vero sapientes tria prima simul collidunt et repro- 
bant, et quartum propter singularem stultitiam propriam lima- 
turam desiderat, ideo primo trium malitiam aperire conabor. 
Sed quamvis auctoritas sit unum de istis, nulla ratione loquor 
de solida et vera auctoritate, quae vel Dei judicio collata est 

' Caecutientes ... I restore the omission firom B. et D., ' omnem sapientiae 
fuJgorem, fastidientes.' 

B 2 



4 OPERIS MAJORIS PARS PRIMA. 

Ecclesiae, vel quae ex merito et dignitate proprie nascitur in 
sanctis philosophis et perfectis prophetis, qui juxta humanam 
possibilitatem in studio sapientiae experti sunt; sed de illa 
auctoritate loquor, quam sine Dei auxih'o violenter usurpave- 
runt multi in hoc mundo, nec ex merito sapientiae, sed cx 
propria praesumptione et desiderio famae, et quam vulgus 
imperitum multis concessit in pemicionem propriam judicio 
Dei justo. Nam secundum scripturas propter peccata populi 
multotiens regnat hypocrita; de sophisticis enim auctori- 
tatibus multitudinis insensatae loquor, quae aequivocae sunt 
auctoritatis, sicut oculus lapideus aut depictus nomen habet 
oculi, non virtutem. 

Capitulum II. 

The first Sed tria reprobat sacra scriptura, sacri doctores condemnant, 

coOTizSbyJ"^ Canonicum vetat, philosophia reprehendit; sed propter 

Cicero, rationes prius tactas de philosophicis allegandis, et quia minus 

Adehad. vulgatae sunt sententiae Philosophorum circa haec tria, eas 

Averrhoes princlpaliter introducam. Similiter vero omnes has tres pestes 

Seneca libro secundo epistolarum prope finem uno sermone 

condemnat. Dicit igitur, *inter causas malorum nostrorum 

est, quod vivimus ad exemplar, nec ratione componimur, sed 

consuetudine abducimur; quod si pauci facerent noUemus 

imitari, cum plures facere ceperint, quia frequentius quam 

honestius, illud facimus, et recti locum tenet apud nos error, 

ubi publicus factus est\* Philosophus vero per totam philo- 

sophiam suam persequens auctoritatem indignam secundo 

Metaphysicae causas humani erroris asserit praecipuas con- 

suetudinem et populi testimonium ^' Et iterum Seneca libro 

de vita beata dicit, *Nemo sibi solum errat, sed alieni erroris 

causa et auctor est, versatque nos et praecipitat error, et 

ah*enis perimus exemplis^* Et in secundo libro de Ira, 

' The passage is in the laard letter (lib. xx. Ep. 8, ed. Haase). Part of the 
quotation is slightly condensed from the original, which runs, ' Cum plures 
facere coepenint, quasi honestius sit quia frequentius, sequimur.* In the la.st 
sentence Jebb substitutes certi for recti. 

' Met. lib. i. (minor), cap. 30/8' dMpodcus «rard rd i$ri avftfiaiifovinr' &s ydp 
«t^uAifi«y oCren d{iov/ity XiyiffBcu, et seq. 

' Seneca, Dialog, vii. cap. i. 



CAUSAE ERRORIS. 5 

*propter malitiam consuetudinis,' ait, 'difficulter reciduntur 
vitia, quae nobiscum creverunt *.' Et in libro de vitae beati- 
tudine contra vulgi sententias refert, 'Nulla res majoribus 
malis nos implicat, quam quod ad rumorem componimur, 
optima rati ea quae magno assensu recepta sunt, nec ad 
rationem sed ad similitudinem vivimus. Inde est ista tanta 
coacervatio aliorum supra alios ruentium. Quod enim in 
strage homini magna evenit, cum se populus ipse premit, 
nemo ita cadit ut non alium in se attrahat, primique sunt 
exitio sequentibus.' Et iterum dicit in eodem, ' Stat contra 
rationem defensor mali sui populus' ; et infra, ' Non tam bene 
cum rebus humanis agitur, ut meliora pluribus placeant,' et 
sequitur, ' argumentum pessimi turba est V Et Marcus Tullius 
tertio de quaestionibus Tusculanis ait, * Cum magistris traditi 
sumus, ita variis imbuimur erroribus, ut vanitati veritas, et 
opinioni confirmatae ipsa natura cedat V Atque in LucuUo 
dicit, 'quidam obsecuti amico cuidam aut una cum aliquo 
quem audierunt oratione capti, de rebus incognitis judicant, 
et ad quamcumque sunt disciplinam quasi tempestate delati^ 
tanquam ad saxum inhaerescunt ; plerique errare malunt, 
eamque .sententiam quam amaverunt defendere, quam sine 
pertinacia perquirere quid constantissime dicant *.' Et propter 
pravitatem consuetudinis queritur in primo de divina natura, 
* non pudet speculatorem naturae ab animis consuetudine 
imbutis petere testimonium veritatis */ Et contra vulgi sen- 
sum dicit proemio secundi quaestionum, philosophia * est 
paucis contenta judicibus, multitudinem ipsam consulto fugiens, 
eique suspecta et invisa®,' et in eodem libro ait, ' laudabiliora 
mihi videntur omnia quae sine populo teste fiunt '^.' Sed alii 
divisim haec tria persequuntur. Nam in libro Quaestionum 
Naturalium Alardi ^ quaeritur de auctoritate fragili : ' Quid est 

> Seneca, DiaL iv. x8. 

* These passages are from Seneca, Dial. vit. i and a. 
' Cic Tusc. Disput. lib. tfi. cap. i. 

* Academ. Priorum^ lib. ii. 3. This is a selection of two passages from the 
chapter. The quotation is not entirely accurate. 

^ De Deorum Naiura, i. 30. * Tusc. Disp. lib. il cap. i, § 4. 

^ Lib. ii. cap. 96, § 64. 

' Jebb has Mardi, a mistake whicb, if he had had the Oxford MSS. before 



6 OPERIS MAJORIS PARS PRIMA, 

aliud auctoritas hujusmodi quam capistrum ? Ut bruta quippe 
animalia capistro ducuntur, nec cui nec quo ducantur dis- 
cernunt, sic nos paucos bestiali crudelitate captos ligatosque 
auctoritas ipsa in periculum ducit/ Et in libro de Dei aeter- 
nitate, 'qui elegerit alteram partem quaestionis propter 
amorem consuetudinis non potest recte discernere veram 
opinionem^.' Et Averroes in fine secundi Physicorum dicit, 
'Consuetudo est maxima causa impediens a pluribus rebus 
manifestis. Quemadmodum enim consueto ad aliquas opi- 
niones licet nocivas, erunt ei faciles, ^et ideo credit eas esse 
utiles; similiter cum fuerit assuetus credere sermones falsos 
a pueritia, erit illa consuetudo causa ad negandum veritatem, 
sicut quidam tam assueti fuerint comedere venenum, quod 
factum est eis cibus/ Et idem Averroes vult secundo Meta- 
physicae *quod opposita principionim cum fuerint famosa 
sunt magis receptibilia a multitudine consequentibus testi- 
monia multorum quam ipsa principia.' Atque Hieronymus 
in prologo quinti libri super Jeremiam asserit, *veritatem 
paucis contentam esse, et hostium multitudine non terreri.* 
Johannes quoque Chrysostomus super Matthaeum dicit, quod 
a veritate nudos se esse professi sunt, qui multitudine se 
arraaverunt. 

CAPITULUM III. 

Thcyare Quod pcr auctoritates probatum est experientia cujuslibet 
practicair ^ertius dijudicatur. Nam experimur in nobis et in aliis quod 
experiencc. haec tria, ut in pluribus amplectuntur mala, frequentius falsis 

him, he would have avoided. The writer referred to is Adelard of Bath, who 
lived in the early part of the twelfth century. He fills an important place in 
the history of mediaeval science. He was the first translator of Euclid into 
Latin ; not, however, from Greek but from Arabic. A more complete translation 
was made in the foUowing century by Campano. [See Weissenborn, Abhand- 
lungen aur GeschichU der Mathetnatik, Drittes Heft, Leipsic, 1880, pp. 141 -166.] 
Adclard studied in the Schools of Tours and Laon ; and subsequently travelled 
in Greece and Asia Minor. The passa^e here cited is from the sixth chapter 
of his Quaeshoties NatunUeSf a work full of audacious and original speculation. 
In Bacon's mathematical treatise, as yet unpublished, he is frequently men- 
tioned, always under the name Alardus. [See Sloane MSS. 2156, ff. 73-95.] 
' I do not know what work is here referred to. 



CAUSAE ERRORIS, 7 

adhaerent Quod si aliquando bonis et veris implicentur, fere 
semper sunt imperfecta, et debilem gradum continent sapien- 
tiae. Matris quidem opera ut in pluribus sequitur filia, patris 
natus, domini servus, regis subditus, praelati bajulus, magistri 
discipulus. Quia familiare est filiis Adae sibi auctoritatem 
vindicare et sua exempla spargere in lucem. Nam omnes 
homines secundum Aristotelem quarto Ethicorum amant sua 
opera, ut parentes natos, et poetae metra, et sic de aliis. £t 
ideo multi nimia licentia scribendi usi sunt, adeo ut pravis et 
bestialibus viris insinuare non dubitaverunt, cur chartas non 
impletis, cur a tergo non scribitis. Et hi sunt sicut pastor 
claudus et caecutiens cum ovibus multis, quas errantes per 
devia falsitatis nec possunt nec sciiint ad saniora sapientiae 
pascua revocare, et sunt similes avibus, qui optant sine alis 
volare, prius de magisterio praesumentes, quam boni discipuli 
gradum adepti sunt, quum necessario tot incidunt in errores, 
quod otiosi comparatione ipsorum reputant se felices; sicut 
quando multi currunt in stadio, ille quem desperatio currere 
non permittet, quantumcunque sibi videatur pemitiosum, se 
tamen felicem reputat comparatione illius, qui currens cadit 
in foveam invisam. £t ideo videmus fide oculata quod pro 
uno exemplo veritatis tam in scientia quam in vita -sunt plus 
quam mille falsitates. Mundus enim plenus est hujusmodi 
exemplis, atque unum exemplum verae perfectionis decem 
millia imperfecta invenit de facili. Natura enim in numeris 
formavit nobis perfectionis et imperfectionis documentum. 
Nam tum numerus perfectus ^ dicitur, cujus partes aliquotae 
ipsum praecise constituunt, et non est nisi unus infra denarium, 
viz. senarius ; et unus inter 10 et 100, ut 28 ; et unus inter 100 
et 1000, ut 496; et unus inter 1000 et 10000 ut 8128 ; et sic 
ultra; et utinam sic esset inter homines, et hoc humano 
generi sufficeret. Sed nunquam fuit hoc nec in vita nec in 
scientia, neque erit usquam in finalem peccati destructionem, 
quoniam non solum est raritas eorum, qui in omni veritate et 
scientia perfecti sunt, sed eorum qui ad perfectionem unius 
veritatis vel scientiae devenerunt. Primi sunt et erunt et 

* Whcn a°"« is a prime number, Uien a**** (a« - 1) is a perfect number, as 
6, aS, 496, BiaS, &c 



8 OPERIS MAJORIS PARS PRIMA. 

fuerunt semper paucissimi. Nam sunt vere perfecti, sed de 
loooo hominum unus non invenitur sic perfectus nec in statu 
vitae neque in professione sapientiae; utinam de secundo 
genere perfectorum infra denarium unus esset, et sic ultra, ut 
perfectio numerorum in hominibus conservaretur. Sed non 
est ita, imo longe aliter invenitur. Similiter de consuetudine 
probamus per experientiam in actibus nostris, quod nunc 
datum est in exemph's. Revolvat quilibet vitam suam ab 
infantia sua, et inveniet quod in pluribus ejus operibus faciHus 
mala et falsa duxit in consuetudinem. Nam in bonis et veris 
identitas humanae fragilitati mater est satietatis, et delectatur 
miser homo in varietate utilium secundum sententiam auctori- 
tatum quas in principio allegavi ; e contrario quidem in mah"s 
et falsis ac nocivis sibi et aliis. Nam ut in pluribus actibus, 
nisi gratia specialis et privilegium divinum in ah'quibus 
perfectis obtinet, humana corruptio diligenter continet ea, 
quae veritati et saluti sunt contraria ; nec taedio aflficitur in 
peccati continuatione, nec fastidium de facili invenit in rebus 
variis. Quod si aliquis a juventute applicetur ad vitae et 
scientiae veritatem, hic ut in pluribus actibus continet imper- 
fectionem, et in ea jocundatur, perfectio enim contristat eum 
frequentius ; nam paucissimos delectat, et maxime in virtutum 
et scientiarum plenitudine, et ideo accidit quos aetas juveniHs 
vix cavet ab errore, et senectus cum summa difficultate ad 
. perfectionem in aliquo transcendit. De vulgo enim idem 
judicium est. Nam multitudo generis humani semper erravit 
in Dei veritate, et paucitas Christianorum recepit; atque 
scimus quod plebs Christianorum imperfecta est. Nam 
paucitas sanctorum hoc ostendit. Similiter de philosophica 
doctrina, vulgus enim semper caruit sapientia philosophiae. 
Brevis enim philosophorum numerus hoc declarat. Et 
vulgus quidem philosophantium imperfectum semper re- 
mansit. Nani de famosis philosophus solus Aristoteles cum 
sua familia vocatus est judicio omnium sapientum, quoniam 
ipse omnes partes philosophiae digessit secundum possibili- 
tatem sui temporis, sed tamen ad Anem sapientiae non 
pervenit, sicut satis manifestabitur inferius. 



CAUSAE ERRORIS. 9 

Capitulum IV. 

Sed tamen quantumcunque fragilis sit auctoritas, nomenofthcse 
habet honoris, et consuetudo violentior est ad peccatum quam ^}^^i„ 
ipsa ; utraque autem earum impetuosior est sensus vulgi. prejndice 
Nam auctoritas solum allicit, consuetudo ligat, opinio vulgi potent™^^^ 
obstinatos parit et confirmat. Consuetudo autem est altera 
natura, ut dicit philosophus libro de memoria et reminiscentia^, 
et in libro Problematum, et ideo majorem violentiam quam 
auctoritas inducit. Unde philosophus 10™** Ethicorum sen- 
tentiae Jeremiae de pelle Aethiopum adhaeret, dicens, * quod 
impossibile est vel difficile eum, qui per consuetudinem malam 
induratus est, mutari ad bonum.' £t Sallustius in Jugurthino 
sensum Solomonis profert, cum ait, 'ubi adolescentiam 
habuere, ibi senectutem agunt.' Sententia quidem vulgi 
caeteris improba magis est. Nam, ut ait Seneca tertio 
Declamationum libro, ^ multitudo semel mota modum servare 
non potest ' ; propter quod Johannes Chrysostomus super 
Matthaeum dicit ' convenerunt ut multitudine vincerent quem 
ratione superare non poterant.' Sic considerandum est dili- 
genter quod vulg^s imperitum non solum violentius est ad 
persuasionem mali quam reliqua duo, sed stultum est et magis 
elongatum a fine sapientiae. Nam exemplum perfectionis 
trahitur ab aliquo in consuetudinem, sed vulgo sufficit ut non 
erret. In nuUo enim statu Ecclesiae requiritur ut ejus per- 
fectionem teneat multitudo. Nam et apud religiosos paucitas 
figitur in centro perfecticmis suae et multitudo vagatur in 
circumferentia. Sic est in statu multorum secularium, ut 
cemimus ad oculum evidenter. Turba enim sicut cum Moyse 
non ascendit in montem, sic nec cum Christo in transfigura- 
tione Christi multitudo discipulorum assumpta est, sed tres 
electi specialiter. £t cum magistrum perfectionis Christum 
turba secuta est per duos annos praedicantem, postea demisit 
eum, et in fine clamavit^ ' Crucifige.' Nam vulgus nihil per- 
fectum continuare potest, utinam enim vita, nec in studio 
errasset. £t sicut nos hoc videmus in veritate fidei, sic in 
professoribus philosophiae. Nam semper sapientes contra 

' De Mentaridf cap. a &ffwtp ySip ^vats Ijiff t6 i$os. 



lo OPERIS MAJORIS PARS PRIMA. 

vulgus divisi sunt, et arcana sapientiae non toti mundo sed 
plebi philosophantium revelaverunt. Quoniam sapientes 
Graeci nocturnis vigiliis congregati vacabant sine vulgo 
collationibus sapientiae, de quibus A. Gellius scribit in libro 
Noctium Atticarum, i. e. collationum sapientiae nocturnalium, 
quas sapientes Attici, i. e. Athenienses celebrabant ut multi- 
tudinem- vitarent. In quo etiam dicit *stultum est asino 
praebere lactucas, cum ei sufficiant cardui/ loquens de vulgo, 
cui rudia et vilia et imperfecta sapientiae sufficiurit alimenta. 
Nec oportet margaritas spargi inter porcos ; nam rerum 
majestatem minuit, qui vulgat mystica: nec manent secreta, 
quorum turba est conscia, sicut in libro Gemmarum edocetur. 
Atque Aristoteles in libro secretorum ^ dicit, * se fore fractorem 
sigilli coelestis, si secreta naturae vulgaret.' Et propter hoc 
sapientes licet darent in scriptis radices arcanorum sapientiae, 
tamen ramos et fructus vulgo philosophantium non dederunt 
Nam vel omiserunt scribere, vel per sermones figurativos et 
multis modis, de quibus non est ad praesens dicendum, 
occultaverunt. Quoniam secundum sententiam Aristotelis 
libro secretorum et Socratis magistri sui, secreta scientiarum 
non scribimus in pellibus caprarum et ovium, ita quod a vulgo 
valeant aperiri. Sapientissimi enim et maxinne expcrti 
multotiens maximam difficultatem in libris reperiunt anti- 
quorum. Et cum philosophus dividat probabile primo libro * 
Topicorum, separat vulgus a sapientibus : Nam dicit probabile 
esse quod videtur, vel pluribus, vel sapientibus ; sub omnibus 
enim comprehenduntur vulgus et sapientes communiter, ergo 
per plures vulgus designatur; quia de consortio sapientum 
non est ipsum vulgus insensatum. Et hoc accidit ei non solum 
propter sui propriam stultitiam, sed quia in pluribus caput 

* This work was perhaps the most widely diffused of the apocryphal writings 
current in the middle ages on Aristotle and Alexander. It was translated from 
the Arabic by a certain Philip, who dedicates the translation to Guido of 
Valence, archbishop of Tripoli, with the remark that the treatise was addressed 
by Aristotle to Alexander, wbo wished the philosopher to accompany him on 
his Eastem expedition. It is sometimes spoken of as Uber de regimine prindpHmi 
also as liber decem scientiarMm, Bacon refers to it frequently, and wrote 
a copious commentary on it, which is preserved among the Tanner MSS. in 
the Bodleian (ii6). 

* Top» lib. L cap. a, § 7. 



CAUSAE ERRORIS. ii 

recipit languidum et infirmum, quod erroribus et proclive est 
et auctor imperfectionis cujus nutu ducitur in omnem eventum. 
Et ideo vulgus imperitum nunquam ad perfectionem sapientiae 
potest ascendere, nam nescit uti rebus dignissimis: quas si 
aliquando casu contingat omnia in malum convertit, et ideo 
justo Dei consilio ncgatae sunt ei viae perfectionis, et optime 
secum agitur quando permittitur non errare. Nam suum 
nomen ostendit omnia quae praedicta sunt, et apud omnes 
auctores vocatur vulgus imperitum vel insensatum. Imperitia 
vero in errore et in imperfectione consistit, et ideo vulgo 
familiaris est error et imperfectio. Nam multi sunt vocati, 
pauci vero electi ad veritatis divinae receptionem, et similiter 
philosophicae. Quare Philosophus dicit secundo Topicorum, 
quod sentiendum est ut pauci, licet loquendum sit ut plures ; 
quia stultitiam vulgi aliquando simulare prudentia summa 
aestimatur, praecipue cum est in furore suo. Ex his omnibus 
colligitur malitia et stultitia horum trium et damnum humani 
generis infinitum, et ideo suspecta sunt in omni causa, nec est 
eis confidendum : et maxime vulgi sensus est negligendus 
propter dictas speciales rationes, non quia aiiquando cadant 
supra vera, sed quia ut in pluribus falsis implicantur. Et 
rarissime exemplum et consuetudo perfectionem habent, 
vulgus autem nunquam pertingit ad eam, ut prius explana- 
tum est. 

Capitulum V. 

Munimen vero ad defensionem contra haec habere non We are 
possumus nisi mandata et consilia Dei ac scripturae suae et ^^^^^ 
Juris Canonici, sanctorum et philosophorum et omnium them by 
sapientum antiquorum, sequamur. Et si his mandatis et and^y Uie 
consiliis adhaereamus, non possumus errare, nec debemus ^^^^°^ 
in aliquo reprobari. In praedictis igitur per philosophum ancients. 
principaliter all^atum est ostendere horum pravitatem et 
stultitiam, propter quas ipsa possemus et debemus evitare, sed 
propter causas assignatas de inducendis philosophorum testi- 
moniis silui fere in aliis ; nunc autem possum invenire con- 
similia testimonia, in quibus consilium vel mandatum de 
obviando istis expressius habetur. Contra igitur sensunx 



12 OPERIS MAJORIS PARS PRIMA. 

vulgi teneamus mandatum Exodi, ' Non sequeris turbam ad 
faciendum malum ; nec in judicio plurimorum adquiesces 
sententiae, ut a vero devies.' Et consilium TuUii in fine ^ de 
quaestionibus impleamus dicentis, ^ Tu autem etsi in oculis sis 
multitudinis, tamen in ejus judicio stare noli^ nec quod ipsa 
putet id putare pulcherrimum.* Et Seneca libro de copia 
verborum invitat nos et consolatur recedentes a via multi- 
tudinis,dicens,*Nondum felix es, si nondum turba te deriserit/ 
Et contra consuetudinem impleamus consilium Cypriani, * Con- 
suetudo sine veritate vetustas erroris est, propter quod relicto 
errore, sequamur veritatem/ Et Augustinus praecipit quod 
' ' veritate manifesta, cedat consuetudo veritati, quia consuetu- 
dinem veritas et ratio semper excludit.' Et Isidorus, * Usus 
auctoritati cedat ; pravum usum lex et ratio vincat.' Et ideo 
TuUius de immortalitate animae kudans et extollens eos, qui 
fugiunt consuetudinem dicit ^magni animi est cogitationem 
a consuetudine revocare.' Nomcn autem auctoritatis favorabile 
est. Et ideo majores nostri venerandi sunt, sive habeant 
auctoritatem veram sive apparentem, quae est auctoritas ducum 
vulgi. Et' contra usum apparentis auctoritatis non solum 
propria sunt consilia et mandata secundum vias Dei et sanc- 
torum et philosophorum et omnium sapientum, sed quicquid 
contra vitia humanae fragilitatis apud auctores veros dici 
potest, commune est eis qui auctoritate abutuntur praesumpta. 
Et ideo si consilia et mandata habemus contra defectus 
verorum auctorum multo magis contra abutentes. Sed quia 
auctores veridici, ut sancti et philosophi principales, juverunt 
nos in consideratione veritatis, ideo regratiandum est eis, sicut 
Aristoteles primo Metaphysicae regratiatur suis praedecessori- 
bus, et in fine Elenchorum ^ de inventis multis ipsemet cupit 
habere grates. Qui vero prima principia jecerunt, cis non 
solum rcgratiandum, sed quasi totum cum quadam reverentia 
ascribendum. Secundum quod Seneca vult tertio ^ naturalium, 
' si quid a posterioribus inventum est, nihilominus referendum 

^ The word secundi seems omitted. The passagc is in Tusc, Disp. iL a6. 
* De Soph. EUnck. xzxiv. § 91 

' The passage is not in the third, but in the sixth book, cap. 5. It is not 
very accurately quoted. 



CAUSAE ERRORIS, 13 

antiquis, quia magni animi fuit rerum latebras primitus dimo- 
vere, et plurimum ad inveniendum contulit, qui speravit 
posse reperire, et quamvis propter humanam fragilitatem in 
multis defecerunt, tamen excusandi sunt/ Nam in libro 
memorato ait Seneca, 'cum excusatione veteres audiendi 
sunt.' 

Capitulum VL 

Sed quoniam propter peccatum originale, et propria cujus- The wisest 
libet peccata partes imaginationis laesae sunt, (nam ratio liabie to 
caecutiens est, memoria fragilis, ac voluntas depravata; et^"*^*^- 
verum et bonum uno modo sunt, falsum autem cuilibet vero 
oppositum et malum cuilibet bono contrarium infinitis modis 
variantur; quia ut.philosophus secundo Ethicorum exempli- 
ficat, facile est diverti a signo dato propter multiformem 
declinationis possibilitatem, sed veritas et virtus sunt in 
puncto ; infinitae etiam sunt veritates, virtutesque, atque 
innumerabiles gradus in qualibet veritate et virtute,) mani- 
festum est quod mens humana non sufficit dare quod neces- 
sarium est in omnibus, nec potest in singulis vitare falsum 
nec malum. £t ideo ad auctorum dicta verorum potest 
convenienter addi et corrigi in quampluribus. Et hoc egregie 
docet Seneca in libro quaestionum naturalium ; quoniam libro 
tertio ^ dicit, * opiniones veteres parum exactas esse ; et rudes 
circa verum adhuc errabant; nova erant omnia primo ten- 
tantibus, postea eadem illa limata sunt ; nuUa res consummata 
est, dum incipit.' Et in quarto* libro dicit, ' veniet tempus, 
quo ista quae latent nunc, in lucem dies extrahet, et longioris 
aevi diligentia. Ad inquisitiones tantorum una aetas non 
sufficit. Multa venientis aevi populus ignota nobis sciet, et 
veniet tempus, quo posteri nostri tam aperta nos nescisse 
mirentur.' Et ideo dicit in prologo majoris voluminis, quod 
nihil est perfectum in humanis inventionibus et infert, quanto 
juniores tanto perspicaciores, quia juniores posteriores succes- 
sione temporum ingrediuntur labores priorum. Et cum jam per 
causam et auctoritatem verificatum est quod volo, nunc tertio 

* /(t)c ciVL vi. 5. • Nat, Quaest, vii. 25. 



14 OPERIS MAJORIS PARS PRIMA. 

per effectum probabo. Nam semper posteriorcs addiderunt ad 
opera priorum, et multa correxerunt, et plum mutaverunt, 
sicut maxime per Aristotelem patet, qui omnes sententias 
praecedentium discussit. Et etiam Avicenna et Averroes 
pUira dc dictis ejus correxerunt. Ad haec reprehenditur de 
mundi aetemitate, quam nimis inexpressam reliquit; nec 
mirum, cum ipsemet dicit se non omnia scivisse. Nam quadra- 
turam circuli se ignorasse confitetur, quod his diebus scitur 
veraciter. Et cum ignoravit hoc, multo magis majora. Ac 
Avicenna, dux et princeps philosophiae post eum, ut dicit 
commentator super causam de Iride in libro Metaphysicae 
Aristotelis, et opera in totam philosophiam ab eo digesta, 
sicut ab Aristotele, hoc manifestant, dixit se materiam Iridis 
ignorasse, sicut praecedens commentator fatetur. Et in tertio 
physicorum se ignorasse unum ex decem praedicamentis, viz. 
praedicamentum habitus, dicere non veretur. Et proculdubio 
in libro de philosophia vulgata errores et falsa continentur, ut 
in undecimo Metaphysicae ponitur error de mundi produc- 
tione, in quo dicitur quod Deus propter infinitam unitatem 
quam habet, et ne recipiat varietatem dispositionum, non potest 
creare nisi unum, scilicet, angelum primum, qui creavit secun- 
dum cum coelo primo, et secundus tertium cum coelo secundo, 
et ultra. Et cum in undecimo ponit omne peccatum habere fines 
su? j purgationis in alia vita, et animas peccatrices redire ad 
gioriam, manifeste errat, et sic in multis. Et Averroes, maximus 
post eos, in multis redarguit Avicennam ; et sic sapientes nostri 
eum in pluribus conigunt et non immerito, quia proculdubio 
erravit in muitis locis, quamvis in aliis optime dixit £t st 
isti majores erraverunt, multo fortius juniores. Quoniam 
autem in errores inciderunt, multo magis defecerunt in neces- 
sariis, superflua et inutilia cumulantes, dubia et obscura et 
perplexa spargentes ; et haec omnia in libris eorum manifesta 
sunt, et per effectum in nobis probantur. Nam tanta difii- 
cultate videndi veritatem premimur et vacillamus, quod fere 
quilibet philosophorum contradicit alii, ita quod vix in una 
vanissima quaestione vel in uno vilissimo sophismate vel una 
operatione sapientiae, sicut in medicina, et chirurgia, et aliis 
operationibus secularium, unus cum alio concordat. 



CAUSAE ERRORIS. 15 

Sed non solum philosophi immo sancti aliquid humanum in 
hac parte passi sunt Nam ipsimet retractaverunt dictorum 
suorum quamplurima. Unde Augustinus, qui major in in- 
quisitione veritatum occultarum reputatur, fecit librum de 
retractatione eorum, quae non bene praedixerat. Et Hierony- 
mus super Isaiam, et alii plures suam non verentur retractare 
sententiam. Nam celeritate dictandi in transferendo pluries se 
confitetur deceptum fuisse, et multis aliis modis ; et sic omnes alu 
doctores fecerunt. Sancti etiam ipsi mutuo suas correxerunt 
positiones et sibi invicem fortiter resistebant. Etiam Paulus 
Petro resistebat, sicut ipsemet confitetur. Et Augustinus 
Hieronymi sententias reprehendit, et Hieronymus Augustino 
in pluribus contradicit. Haec exempla eorum manifesta sunt, 
ut inferius exponetur, et posteriores priorum dicta correxerunt. 
Nam Origenem maximum doctorem secundum omnes in 
multis posteriores reprobant, quia inter caetera posuit errorem 
Avicennae de animabus peccatricibus, quod nulia finaltter 
damnabitur. Et cum multi doctores sancti et famosi ex- 
posuerunt Israel, ut dicatur vir videns Dmm^ venit Hieronymus 
super Genesim et probat falsam esse expositionem ^ per rationes 
irrefragabiles, sicut inferius exponetur. Unde dicit, ' quamvis 
auctoritatis sint, et eorum umbra nos opprimat qui Israel 
virum videntem Deum interpretati sunt, tamen magis con- 
sentimus Deo vel angelo qui hoc nomen imposuit, qttam 
auctoritati alicujus eloquentiae secularis.' Et doctores catholici 
in studiis solemnibus constituti nunc temporis in publicis multa 
mutaverunt, quae sancti dixerunt, eos pie exponentes ut 
possunt, salva veritate. 

Capitulum VII. 

Quoniam igitur haec ita se habent, non oportet nos ad- Piato, 
haerere omnibus quae audimus et legimus, sed examinare Aogiwtinc, 
debemus districtissime sententias majorum, ut addamus quae Boetius, 

. , . . prefcrred 

eis defuerunt, et corngamus quae errata sunt, cum omnitnithto 

authority. 
' Nevertheless in Jerome^s Commentaries on Isaiah and on Amos (voL iv. 
p. 07, and voL vi. p. 1039 of Migne*s ed.) the interpretation vidtns Dtum is 
accepted. 



i6 OPERIS MAJORIS PARS PRIMA. 

tamen modestia et excusatione. £t ad hanc audaciam erigi 
possumus, non solum propter necessitatem, ne deficiamus vel 
crremus, sed per exempla et auctoritates, ut in nuUo simus 
reprehensibiles de praesumptione, Nam Plato dicit, * Amicus 
est Socrates, magister meus, sed magis est amica veritas/ 
Et Aristoteles dicit, * se magis velle consentire veritati, quam 
amicitiae Platonis, doctoris nostri/ Haec ex vita Aristotelis 
et primo Ethicorum, et libro secretorum, manifesta sunt. 
Et Seneca dicit libro de quatuor virtutibus cardinalibus, 
' Non te moveat dicentis auctoritas ; non quis, sed quid/ Et 
Boetius libro de disciplina scholarum, *stultum est magistra- 
tus orationibus omnino confidere, nam primo credendum est, 
donec videatur quid sentiat ; postea est fingendum eundem 
in dicendo errasse, si forte reperire queat discipulus, quod 
expresse objiciat sedulitati magistrali.' Et Augustinus dicit 
ad Hieronymum, * quod solos auctores scripturae sacrae vult 
credere in scribendo non errasse, sed in scripturis aliorum, 
quantumcunque sanctitate et doctrina polleant, non vult 
verum putare, nisi per canonem et alios auctores vel per 
rationes sufiicientes possint probare quod dicunt.' Et ad 
Vincentium dicit * negare non possum, nec debeo, sicut in 
ipsis majoribus, ita multa esse in tam multis opusculis meis, 
quae possunt justo judicio et nulla temeritate culpari ^' Et 
in prologo libri tertii de Trinitate dicit, ' sic meis libris nisi 
certum intellexeris, noli firmum tenere.' Item ad Fortunatia- 
num ; ' neque quorumlibet disputationes quamvis catholicorum 
et laudatorum hominum veluti scripturas canonicas habere 
debemus, ut nobis non liceat, salva honorificentia quae illis 
debetur hominibus, aliquid in eorum scriptis improbare atque 
respuere, si forte invenerimus quod aliter senserint quam 
veritas habeat, divino adjutorio vel ab aliis intellectum vel 
a nobis. Talis ego sum in scriptis aliorum, quales volo esse in- 
tellectores meorum ^' Si igitur propter necessitatem vitandae 
falsitatis et consequendi perfectiorem statum sapientiae possu- 
mus, et debemus, et consulimur per sanctos perfectos et philo- 

* Aug. deAmma, lib. iv. cap. i. 

* Aug. Ep. cxlviii. § 15, voL ii p. 6a8, Migne's Ed. The correspondeiit 
was not Fortunatus the Manichaean, as Jebb has it 



CAUSAE ERRORIS. 17 

sophos dignos, ut eorum dicta mutemus loco et tempore. et ad 
eorum sententias addamus ; multo fortius licentiamur ad hoc 
et cogimur in eis, quae vulgi sunt et eorum qui vulgo praesunt 
imperito, praecipue cum capita multitudinis istius temporis 
non attingunt ad dignitatem auctoritatis sanctorum et philo- 
sophorum magnorum nec sapientum antiquorum, quorum 
aliquos nostro tempore conspeximus. 

Capitulum VIII. 

Remedium vero contra haec tria non est, nisi ut totaTheirex- 
virtute auctores validos fragilibus, consuetudini rationem, sen- s^^\^^^ 
sibus vulgi sententias sanctorum aut sapientum reponamus, imitate. 
et non coniidamus in argumento triplicato, scilicet, hoc exem- 
ph'iicatum est, vel consuetum, aut vulgatum, igitur tenendum. 
Patet enim ex praedictis secundum sententias sanctorum et 
omnium sapientum, quod longe magis sequitur oppositum 
conclusionis ex eisdem praemissis. Et licet totus mundus 
sit his causis erroris occupatus, tamen audiamus libenter 
contraria consuetudini vulgatae. Nam hoc est magnum 
remedium horum malorum, secundum quod Averroes dicit 
in fine secundi physicorum, quod mala consuetudo auferri 
potest per consuetudinem audiendi contraria. Nam multum 
operatur in opinione, quae est per consuetudinem, audire res 
extraneas, quod confirmat per effectum, dicens, quod ideo 
opinio vulgi est fortior quam fides philosophantium, quia 
vulgus non consuevit audire diversa, sed philosophantes multa 
audiunt. Propter quod igitur Vestra Sapientia non miretur^, 
si contra consuetudinem vulgi et exempla vulgata laborem. 
Nam haec est via sola perveniendi ad considerationem veri- 
tatis et perfectionis. 

Capitulum IX. 

Non solum quidem hae causae generales sunt malorum in The fonrth 
studio et in vita, sed quarta nequior his tribus est, similiter ^j^ ^^ 
communis in omni statu, et apud quamlibet personam regnare conccit of 

^ J. adds the words ' nec indignetur auctoritati,' which are not very intel- 
ligible. O. omits them. 

VOL. L C 



i8 OPERIS MAJORIS PARS PRIMA. 

knowledge, dcmonstratur, Conjunxi quidem praedictas tres causas, et 
them^t propter hoc quod sapientes eas saepius conjungunt et sepa- 
pemicious. ravi hanc ab illis propter malitiam principalem. Haec enim 
est singularis fera, quae dcpascit et destruit omnem rationem, 
quae est apparentis sapientiae desiderium, quo fertur omnis 
homo. Nam quamcunque parum sciamus et licet vile, idem 
tamen extoUimus ; celebramus etiam multa quae ignoramus 
ubi possumus occultare ignorantiam, et scienter ostendimus, 
ut de nihilo gloriemur. Et quicquid nescimus, ubi scientiam 
ostentare non valemus, negligimus, reprobamus, reprehendimus 
et adnihilamus. ne videamur aliquid ignorare, quatenus saltem 
mundo muliebri et fuco meretricio nostram ignorantiam 
infami remedio coloremus, unde utilissima et maxima et omni 
decore plena et sua proprietate certissima a nobis per hanc 
viam et ab ah'is relegemus. Haec vero pestis propter mah'- 
tiam absolutam quam habet recepit cumulum suae pravitatis 
in eo, qui est fons et origo causarum trium praedictarum. 
Nam propter zelum nimium sensus proprii et excusandi 
ignorantiam statim exoritur fragih*s auctoritatis praesumptio, 
qua nitimur propria extollere, et reprehendere aliena. Deinde 
cum omnis homo dih*gat opera sua, ut dicit Aristoteles, nostra 
libenter trahimus in consuetudinem. Et cum nemo sibi soli 
errat, sed sententiam suam spargere gaudet in proximos, ut 
dicit Seneca libro secundo epistolarum, nostris adinven- 
tionibus occupamus aHos et eas in vulgum quantum possumus 
dilatamus. Necesse est vero causas universales hic praemitti, 
ad hoc ut error vitetur et veritas relucescat. Nam in morbo 
spirituaU evenit sicut in morbo corporali. Medici enim per 
signa causas proprias et particulares morbi cognoscunt ; sed 
tam hanc quam illas praecedit causarum universalium notitia, 
quas a communibus naturalium medicus habet scire ; quia 
dicit philosophus libro de Sensu et Sensato^, ubi terminant 
principia philosophiae naturalis incipiunt principia medicinae. 
Similiter igitur in cura ignorantiae et erroris, ut veritas sana 
inducatur, ante ipsius propositi exhibitionem requiritur ut 

^ Dt Smsu, cap. X rSnf vtpi ^vcws cl wKuctoi Mtd rw larpSav oi ^Xo- 
«ro^wrcptis rij^ rix^ /urUrrtf, oi ftkv rtXfvrSafftw c2v rd v<p2 larpiKis, ol ^ Itt rS/v 
w€pi ^vc€on dpxprrai wtpi r^ tarpunjs. 



CAUSAE ERRORIS. 19 

signa et caiisae particulares ostendantur; sed prae omnibus 
exiguntur causae universales, sine quibus nec signa aliquid 
ostendunt nec causae particulares demonstrant Nata enim 
nobis est via cognoscendi ab universalibus ad particularia, sicut 
dicit philosophus in principio Physicorum. Nam, ignoratis 
communibus, ignorantur quae post^ communia relinquuntur. 

Haec autem causa quarta multum invaluit ab antiquo, 
sicut nunc improba invenitur quoque in theologicis, sicut in 
philosophia manifesto, per experientiam et exempla. Moyses 
enim simplicissimus recepit sapientiam legis a Deo, contra lllustra- 
quem Pharao et Aegyptii, et populus Hebraeorum, et omnes y^^li '^"^ 
nationes murmurabant, ita quod vix plebs Dei electa hanc Moses, 
sapientiam recipere voluit, et tamen praevaluit lex contra ArUtoUe, 
adversarios, qui neglexerunt et impedierunt sapientiam quam Avicenna. 
didicerunt. Similiter Dominus Jesus Christus omni simpli- 
citate et sine ph'ca falsitatis incedens, et apostoli simplicissimi 
intulerunt sapientiam mundo, quibus satis contradictum erat 
per ignorantiam solam tantae novitatis, et tandem, licet cum 
summa difficultate, sacra veritas est recepta. Deinde sancti 
doctores cum profluvia expositionum legis divinae voluerunt 
dare, et magno impetu aquarum sapientiae ecclesiam irrigare, 
diu reputabantur haeretici, et compositores falsitatum. Nam 
sicut prologi beati Hieronymi in bibliam et ah*a ejus opera 
probant, ipse vocabatur comiptof scripturae et falsarius et 
haeresium scminator, et in tempore suo succubuit, nec potuit 
sua opera in publico promovere; sed tandem post mortem 
suam veritas suae translationis claruit et sua expositio, et per 
omnes ecclesias dilatatae sunt, ita ut nullum vestigium trans* 
lationis antiquae, scilicet LXX interpretum, qua prius usa 
fuerat ecclesia, valeat reperiri. Dum etiam beatissimus Papa 
Gregorius auctoritate functus est, ejus libris non fuit contra- 
dictum : sed post mortem famosi in ecclesia egerunt ad hoc, 
ut comburerentur, et per miraculum Dei pulcherrimum fuerunt 
salvati, et apparuit mundo sapientia cum sua veritate et in 
demonstratione plenissima. Et similiter cucurrit impedi- 
mentum veritatis apud omnes sacrae scripturae doctores ; 
nam renovantes studium semper receperunt contradictionem 

' Not postea, as in J. 
C 2 



ao OPERIS MAJORIS PARS PRIMA. 

et impedimenta, et tamen veritas invalescebat et invalescet 
usque ad dies Antichristi. 

Similiter de philosophia. Aristoteles enim voluit contra- 

dicere prioribus et multa renovare, qui licet sapientissimus 

habuit tamen repulsam, et occultationes suae sapientiae visus 

est usque fere ad haec tempora recepisse. Nam primus 

Avicenna revocavit philosophiam Aristotelis apud Arabes 

in lucem plenam. Vulgus enim philosophantium ipsum 

ignoravit. Pauci enim et modicum philosophiae Aristo- 

telis attigerunt ante tempus Avicennae, qui diu post tempus 

Machometi Imperatoris philosophatus est. Avicenna vero 

praecipuus Aristotelis expositor et maximus imitator multas 

rebe]h'tates passus est ab altis. Nam Averroes major post 

eos et alii condemnaverunt Avicennam ultra modum ; sed his 

temporibus gratiam sapientum obtinuit quicquid dicit Aver- 

roes. qui etiam diu neglectus fuit et repudiatus ac reprobatus 

a sapientibus famosis in studio, donec paulatim patuit ejus 

sapientia satis digna, licet in aliquibus dixit minus bene. 

Scimus enim quod temporibus nostris Parisiis diu fuit contra- 

dictum naturali philosophiae et metaphysicae Aristotelis per 

A^-icennae ct Averrois expositores, et ob densam ignorantiam 

fuenint libri eorum excommunicati, ct utentes eis per tempora 

sads longa. Cum igitur haec ita se habent, et nos modemi 

approbamus viros praedictos tam philosophos quam sanctos ; 

et scimus quod omnis additio et cumulatio sapientiac quas 

dederunt, sunt dignae omni favore, licet in multis ahis dimi- 

nuti sint. et in pluribus superflui, et in quibusdam corrigcndi, 

et in aliquibus explanandi, manifestum nobis est quod illi, 

qui pcr aetatcs singulas impcdiverunt documenta veritatis et 

utilitatis quac oblata fuerunt eis pcr viros praedictos, nimis 

erravcnint, et vitiosi plurimum fuerunt in hac parte ; sed hoc 

fcccrunt propter scientiae extollentiam et proptcr ignorantiam. 

Elrgo in nobis ipsis debcmus facere idcm argumentum, 

ut cum nos respuamus et vitupcrcmus quae ignoramus, 

clamemus hoc essc propter ignorantiae nostrae defen- 

sioncm, ct ut illa modica, quae scimus, sublimius attollamus. 

Permittamus igitur labores introduci congaudcntes vcritati, 

quia proculdubio licet cum difiicultate vcritas sempcr prac- 



CAUSAE ERRORIS. 21 

valebit, donec Antichristus et ejus appareant praecursores. 
Nam semper bonitas Dei est parata sapientiae donum aug> 
mentare per subsequentes, et subsequentium sententias in 
melius transformare. 



Capitulum X. 

Caeterum duo sunt hic discutienda, videlicet, praesumptae Two heads 
scientiae ostentatio, et excusatio ignorantiae infructuosa. ° ' ^ 



error: ex- 
tion 

lOW- 



Propter primum debemus advertere dih*genter, quod cum aggeiai 
infinitae sunt veritates Domini et creaturarum, atque in qua- icdge: 
libet sunt gradus innumerabiles, oportet quod pauca sciantur I»l"at»on 
a quolibet, et ideo de multitudine sdtorum non oportet quic- ance. 
quam gloriari. Et cum intellectus noster se habet ad maxima, 
sicut oculus vespertilionis ad lumen solis, ut prius secundum 
philosophiam allegatum est, oportet quod sint parva quae 
veraciter sciamus; nam pro certo ubi intellectus noster de 
facili comprehendit, illud valde modicum est et vile, et quanto 
cum majori difficultate intellexit, tanto est nobilius quod ad- 
quiritur. Sed tamen omne id super quod potest intellectus 
noster, ut intelligat et sciat, oportet quod sit indignum re- 
spectu eorum, ad quae in principio credenda sua debilitate 
obligetur, sicut sunt divinae veritates et multa secreta naturae 
et artis complentis naturam, de quibus nulla ratio humana 
dari potest in principio; sed oportet quod per experientiam 
illuminationis interioris a Deo recipiat intellectum, videlicet 
in sacris veritatibus gratiae et gloriae, et per experientiam 
sensibilem in areanis naturae et artis expergefactus inveniat 
rationem. 

£t adhuc minora sunt longe quae credimus, quam quae Perfect 
ignoramus, sicut sunt secreta Dei, et arcana vitae aetemae, ^°^j[^5^ 
quae utcunque vidit Apostolus, ad tertium coelum raptus, able by 
nesciens utrum in corpore vel extra corpus, quae tanta sunt, °^* 
ut non liceat homini loqui de illis. £t similiter in rebus 
creatis ; nam ob magnam intellectus nostri difficultatem 
certum est, antequam videatur Deus facie ad faciem nunquam 
homo sciet aliquid in fine certitudinis. £t si per infinita 
seculorum secula viveret in hac mortalitate, nunquam ad 



22 OPERIS MAJORIS PARS PRIMA, 

perfectionem sapientiae in multitudine scibilium et certitudine 
pertingeret. Nam nullus est ita sapiens in rerum naturis, 
qui sciret certificare de veritatibus omnibus quae sunt circa 
naturam et proprietates unius muscae, nec sciret dare causas 
proprias coloris ejus, et quare tot pedes haberet, et non plures 
neque pauciores, nec rationem reddere de membris ejus. Est 
igitur homo impossibilis ad perfectam sapientiam in hac vita, 
et ad perfectionem veritatis nimis est difficih's, et pronus ^ et 
proclivis ad falsa et vana quaecunque; quapropter non est 
homini gloriandum de sapientia, nec debet aliquis magnificare 
et extoUere quae scit. Pauca enim sunt et vilia respectu 
eorum quae non intelligit sed credit, et longe pauciora respectu 
eorum quae ignorat. Et quoniam respectu eorum quae scit 
homo, restant infinita quae ignorat, et sine omni comparatione 
majora et meliora et pulchriora : insanus est qui de sapientia 
se extollit, et maxime insanit qui ostentat et tanquam por- 
tentum suam scientiam nititur divulgare. 
Thesimplc Praeterea quis audet de sapientia gloriari, qui totam me- 
paM^thY' dullam, quam unus quantumcunque studiosus addiscit per 
leamed in viginti vel quadraginta annos et cum maximis expensis et 
labonbus gravissimis, valet uni puero dociU certo scripto et 
verbo sufficienter ostendere per annum unum, vel in minori 
tempore ? Nam boc probavi in puero praesenti, qui in pau- 
pertate magna et modicam habens instructionem, quantitatem 
anni vix ponens in addiscendo, novit tot et tanta quae omnes 
mirantur qui eum cognoscunt. Nam securus dico quod licet 
aliqui sciunt plus de philosophia et linguis, et in diversis 
diversi ipsum excedunt, non tamen inter Latinos sunt qui 
eum ex omni parte transcedunt, et ipse singulis eorum est in 
aliquibus par, et in quibusdam singulos excedit. Nec est 
aliquis inter Latinos quin multa bona valeat ab isto puero 
auscultare. Nec aliquis tam sapiens est cui non sit necessarius 
multis modis. Quamvis omnia didicit meo consilio et regi- 
mine et adjutorio, et multa ipsum docui verbo et scripto, 
tamen me senem in multis transcendit propter meliores ra- 
dices quas recepit, ex quibus potest fructus salubres expectare, 
ad quos ego nunquam pertingam. Quare igitur gloriabor de 

' sic O. J. has multum parvus. 



CAUSAE ERRORIS. 23 

scientia? Non dico, quidam sapientes et experti potuerunt 
per suam virtutem propriam facilius et citius cernere multa 
secreta sapientiae, quam hic puer per seipsum, quia non est 
expertus vires suas, nec percipit quantum novit nec quid 
potest facere juxta fundamenta sibi tradita, sed sicut in 
radicibus excedit alios, ut dictum est, sic si sano et efiicaci 
consilio juxta fontalem plenitudinem quam habet dirigeretur, 
nullus seniorum consequeretur eum in sapientialium profluviis 
rivorum. £t quoniam sapientes se sentiunt magis vacuos 
quam insipientes, vel qui noiunt de ipsis confiteri, ideo vide- 
mus homines quanto sapientiores sunt, tanto humilius se 
inclinare ad doctrinam alterius suscipiendam, nec dedignantur 
simph'citatem docentis, sed ad rusticos, et ad vetulas, et pueros 
se humiliant. Quoniam simplices et idiotae aestimati sciunt 
multoties magna quae latent sapientes, sicut Aristoteles docet 
de somno et vigilia ^, secimdo libro. Nam cum simplicibus est 
sermocinatio Dei secundum scripturam, et experientia reddit 
nos certos in hac parte, quoniam plura secreta sapientiae 
semper inventa sunt apud simplices et neglectos quam apud 
famosos in vulgo. Quia homines famosi in eis occupantur, 
quae vulgantur, et haec non possunt esse magnalia, sicut 
patuit in prioribus ; plura etiam utilia et digna sine compara- 
tione didici ab hominibus detentis magna simplicitate, nec 
nominatis in studio, quam ab omnibus doctoribus meis famosis. 
Proposui igitur Sapientiae Vestrae hoc exemplum, et transmisi 
per eum, non solum propter duas causas superius annotatas, 
sed in argumentum perfectum, ut nuUus glorietur de sapientia, 
nec despiciat simplices qui sciunt proponere ea quae famosis 
hominibus in scientia Deus non concessit, et sciunt renovare 
et revelarc multa secreta, quae sapientes vulgati nondum 
perccperunt. 

Capitulum XI. 

Secundum vitium, quod hic reperitur, est, quod ignorantia Ignomnce 

• 1 ... .. f inost foul 

retmet locum persuasionis, sed cum ventas impugnatur, nefas ^hen it 

^ The reference seems to be to Z>f divm. per stmmum^ cap. 9 mhm ^dp 
cvrtXcrf dy^ponroc wpooparntoi tlai mU ti^Mptipoi, and again, ro w6$oi rovro 
avfifiaivH timV rvxoviri, mU o( roTf ^povi/mr&rois. 



24 OPERIS MAJORIS PARS PRIMA. 

usurpsthc est et puritas malitiae, deinde ignorantiae turpitudo crescit 
Eifowledge. ^^S^^ ^^ clarius revelatur. Crescit quidem, quia nititur a se 
et ab aliis excludere sapientiam ; apertius quidem revelatur, 
quoniam coram Deo et hominibus^ veraciter innotescit hoc 
secundum judicium omnis sapientis ; ergo cum judex teneatur 
habere scientiam causae, non habet homo ignorans auctori- 
tatem judicandi de his quorum habet ignorantiam. Et ideo 
si de illis affirmet vel neget, ejus judicio stari non debet, immo 
ex hoc vehementius resistendum, quod sententia qualiscunque 
feratur ex ignorantia ea auctoritatem non habet: Unde si 
verum diceret, verisimile non esset. Nam, ut dicit Seneca 
libro de virtutibus cardinalibus, nullam auctoritatem habet 
sententia, ubi qui damnandus est damnat. Quapropter sive 
sapientes apud vulgum, seu secundum veritatem, sive bonus, 
sive sanctus affirmet vel reprobet quod ignoret, et maxime 
in excusatione suae ignorantiae, vel ostentatione sapientiae 
apparentis, approbari non debet ex hac parte, sed negiigi et 
contradici, quamvis ex aliis fuerit magnifice collaudandus. 

Capitulum XII. 

Knowledge Hanc vero causam malbrum nostrorum cum aliis tribus ideo 

vaiue^now specialiter introduxi, ut sciamus' nunc, sicut in retroactis tem- 

neglectcd: poribus, multa quae sunt utih*ssima et omnino necessaria, 

Math^- studio absolute considerato et quatuor modis relate prae- 

matics. tactis, ncgari negligi et ex sola ignorantia reprobari. Et pro 

infinitis latius explicandis posterius in singulis partibus sapien- 

tiae, volo nunc aliqua extra praemittere grossiora. Cum enim 

linguarum cognitio et Mathematicae est maxime necessaria 

studio Latinorum, ut tactum est superius, et exponetur loco 

opportuno, et fuit praecise in usu sanctorum et omnium sapi- 

entum antiquorum, nos modemi negligimus, adnihilamus, et 

reprobamus, quia ista et eorum utilitatem nescimus. Deinde, 

si aliqui sapientes et sancti alia neglexerunt aut humana 

fragilitate devicti aut ex causa rationabili, nos praesentis 

temporis obstinate et pertinaciter negligimus et reprobamus, 

fortificantes nostram ignorantiam propter hoc quod sancti et 

^ sic O. J., omnibus sanctis. 



CAUSAE ERRORIS. 25 

sapientes neglexerunt, non volentes considerare quod in omni 
homine est multa imperfectio sapientiae, tam in sanctis quam 
in sapientibus, ut prius evidenter et multipliciter probatum 
est tam per eorum exempla et auctoritates, quam per rationem 
et experientiae certitudinem. Praeterea non solum volumus 
humanam fragilitatem considerare, sed etiam ^ causas ratio- 
nabiles, quas sancti et sapientes multi habuerunt, quare pro 
loco et tempore multa utilia vitaverunt propter abusum homi- 
num in eis, quia ea convertebant ad majoris impedimenta 
utilitatis et salutis. Ne igitur nos simus causa erroris nostri 
et fiat magnum sapientiae impedin^ntum ex eo quod vias 
sanctorum et sapientum non intelligimus, ut expedit, pos* 
sumus auctoritate sanctorum et sapientum antiquorum multi- 
pliciter prius assignata considerare pia mente et animo 
reverenti, propter veritatis dignitatem quae omnibus ante- 
fertur, si sancti et sapientes aliqua quae humanam imper- 
fectionem important protulerunt in quibus seu affirmatis seu 
negatis non oportet quod nos imitemur ex fronte. 

Scimus quidem quod non solum dederunt nobis consilium Wisc mtn 
et liccntiam hoc faciendi, sed conspicimus quod ipsi multa gou^ht to 
posuerunt magna auctoritate, quae postea majori humilitate amend an<i 
retractaverunt ; et ideo latuit in eis magna imperfectio priori- enor. 
bus temporibus. Quod si vixissent usque nunc, multo plura 
correxissent et mutassent. Cujus signum est sicut et argu- 
mentum principalis intenti, quod doctores posteriores quam- 
plurima de sententiis sanctorum mutaverunt, et pie et reve- 
renter interpretati sunt in sensum quem eorum litera non 
praetendit. Praeterea sancti ad invicem fortiter contendebant 
et mutuas positiones acriter mordebant, et reprobabant ut 
taedeat nos conspicere, et supra modum miremur; quod 
evidens est in epistolis beatorum Augustini et Hieronymi, 
et multis aliis. Cum enim Hieronymus comparavit se bovi 
lasso, qui fortius pedem iigit, propter hoc quod jam in studio 
sacro senucrit, et Augustinus fuit junior eo, quamvis episcopus, 
respondit monacho pontifex quod bos senex fortius figit pedes 
non animi vigore sed corporis senectute. Et cum Augustinus 
multa quaereret ab Hieronymo, dicit Hieronymus, * Diversas 

* MSS. have nec, but etiam seems required. < 



26 OPERIS MAJORIS PARS PRIMA. 

tu nominas quaestiones, sed ego sentio meorum opusculorum 
reprehensiones continuas. Fraetermitto salutationes, quibus 
meum demulces caput; taceo de blanditiis, quibus reprehen- 
sionem meam niteris consolari, ut ad ipsas causas veniam ; 
observari legis ceremonias non potest esse indifferens, sed aut 
bonum aut malum ; tu vero bonum, ego malum assero ; dum 
aliud vitas, ad aliud devolveris ; dum enim metuis Porphyrium 
blasphemantem ^ Ebionis haeretici laqueos incurris/ Et talia 
innumerabilia colliguntur ex libris sanctorum, qui tam in 
rebus de quibus est contentio quam in modo reprehensionis, 
multum in scientiis humanae fragilitatis ostendunt, qua affirma- 
bant quod non debebant Sed constat, non ex certa scientia 
hoc fecerunt ; ergo ex apparenti, et aestimata laboraverunt in 
hac parte. 

Capitulum XIII. 

Erroreof Caeterum non solum ex hujus mortalitatis imperfectione 
jJJ^^^* multa reprobant, quibus nos non oportct obstinate inhaerere, 
ignorance immo magis ad eorum honores pie et reverenter interpretari 
ran<nT*S. secundum leges veritatis ; multa etiam et maxtma neglexenint 
ex causis certis. Una est, quia non fuenint translata in 
linguam latinam, nec ab aliquo Latinorum composita, et ideo 
non fuit mirum si illorum non aestimabant valorem. Platonis 
enim libros doctores omnes assumebant in manibus, quia 
translati fuerunt; sed libri Aristotelis.non fuerunt tunc tem- 
poris translati. Nam Augustinus fuit primus translator 
Aristotelis et expositor, sed in minimo et in primo iibellonim 
suorum, videlicet in praedicamentis : nec fuit philosophia 
Aristotelts tunc temporis Graecis philosophis nota, nec 
Arabicis, sicut prius tactum est. Et ideo sancti, sicut et alii, 
negiexerunt philosophiam Aristotelis, laudabant Platonem. 
Et quia intellexerunt quod Aristoteles persccutus est senten- 
tias Platonicas, Aristotelem in multis reprobant, et dicunt 
rationem haercses congregasse; sicut Augustinus dicit in 
libro de Civitate I>ei ipsum, adhuc magistro suo Platone 

■ bUsphenuuiteai om. in J. The passage occurs in £>. cxii. § 16, voL i. 
pi 927 of Mic;nc*s ed. 



CAUSAE ERRORIS. 27 

vivente, multos in suam haeresim congregasse. Sed tamen 
omnium philosophantium testimonio Plato nullam compara- 
tionem respectu Aristotelis noscitur habuisse. Si igitur 
sancti philosophiam ejus vidissent, pro certo ea usi essent, et 
altius extuhssent, quia veritatem non negassent manifestam, 
nec maxima pro minimis dech*nassent. Nam Augustinus 
ipse transtulit Ubrum Praedicamentorum de Graeco in Latiiium 
pro filio suo, et exposuit diligenter, plus laudans Aristotelem 
de hoc nihilo, quam nos pro magna parte suae sapientiae. 
Quoniam in principio didt, * cum omnis scientia et disciph'na 
non nisi oratione tractetur, nullus tamen, o fili mi, in quovis 
genere pollens inventus est, qui de ipsius orationis vellet 
origine principiove tractere; idcirco miranda est Aristotelis 
diligentia, qui disserendi de omnibus cupidus ab ipsius coepit 
examine, quam sciret et praetermissam a cunctis ^ et omnibus 
necessariam.' £t in fine dicit, < haec sunt, fili carissime, quae 
jugi labore assecuti ad utilitatem tuam de Graeco in Latinum 
vertimus, scilicet, ut ex his quoque bonam frugem studii 
a nobis suscipias^.' £t Alcuinus de expositoribus sacrae 
scripturae unus, et magister Caroli Magni, illam translationem 
Augustini de Praedicamentis mire laudavit, et metrico pro* 
logo decoravit in his verbis, 

' Continet iste decem naturae verba libellus, 
Quae jam verba tenent rerum ratione stupenda 
Omne quod in nostrum poterit decurrere sensum ; 
Qui legit, ingenium veterum mirabile laudet, 
Atque suum studeat tali exercere labore. 
Nunc Augustino placuit transferre magistro 
De veterum gazis Graecorum dave Latina, 
Quem tibi, Rex magne, Sophiae sectator, amator, 
Munere qui tali gaudes, modo mitto legendum.' 
Boetius quidem fuit longe post sanctos doctores, qui primus 
incepit libros Aristotelis plures transferre. £t ipse aliqua 
logicalia et pauca de aliis transtulit in Latinum. Nec adhuc 
medietatem, nec partem meliorem habemus. Nam Aristo- 
teles quidem fuit diu ignotus et philosophantibus, nedum aliis, 
et vulgo Latinorum. Caeterum sancti grammaticalia logicalia 

* multis, J. ' Aug;. Categor, cap. z et 22. 



28 OPERIS MAJORIS PARS PRIMA. 

et rhetorica, ct communia metaphysicae multum efferunt, et 
abundanter in sacris utuntur. Unde Augustinus in libro de 
doctrina christiana, a**, 3^ 4° docet ista applicari ad divina, 
ct in aliis locis : nec non et sancti caeteri idem volunt. Sed 
de aliis parum et raro loquuntur, imo multam negligunt et 
negligi edocent aliquando, sicut per Ambrosium patet super 
epistolam ad Colossenses, et per Hieronymum super illam ad 
Titum, et per Rabanum de pressuris ecclesiasticis, ac etiam in 
locis aliis pluribus. Sed constat omnibus philosophantibus 
et theologis scientias has nuUius valoris esse respectu caete- 
rarum nec alicujus dignitatis. Constat omnibus^ si sancti 
habuissent usum scientiarum philosophiae magnarum, nun- 
quam cineres philosophicos in tantum extulissent, et ad sacros 
usus convertissent, quanto enim sanctae scientiae* meliores 
sunt et majores, tanto sunt ad divina aptiores. Sed quia ad 
manus eorum non devenerunt libri nisi grammatici, logici, 
rhetorici et de communibus metaphysicae, ideo his se 
juverunt secundum gratiam eis datam ; et quicquid poterant 
de his laudabiliter extrahere, converterunt copiosius ad legem 
Dei, ut in expositionibus eorum et tractatibus singulariter 
manifestum est, et hoc suo loco planius exponetur ^ 

Capitulum XIV. 

Why the Deinde considerandum est diligenter, quod quamvis multa 

chirch habuissent de majoribus sdentiis, non fuit tempus utendi eis 

negicctcd nisi in duobus casibus, scilicet, astronomia pro calendario, et 

pii osop y. ^^^.^^ pro officio divino. Patet enim per historias, quod 

Eusebius Caesariensis, et beatus Cyrillus, et Victorius et 

Dionysius Abbas Romanus, cujus doctrinam nunc sequitur 

ecclesia per leges astronomiae, et alii ex mandato apostolico 

laboraverunt in hac parte ; sed aliae scientiae majores fuerunt 

negiectae» et praecipue istae quae judicia et opera sapientiae 

magnifica noscuntur continere. £t hujus causa fuit quintuplex. 

Nam philosophia ante Christi adventum dedit leges mundo, 

* Quapropter, J, * sanctis, J, 

' The last part of the sentence is omitted in O. and D. Ltke many othcr 
passages in tbe first thrce parts of the work, it has been supplied from Jul. 



CAUSAE ERRORIS. 29 

praeterquam populo Hebreorum, tam de cultu divino quam 
de moribus et legibus justitiae et pacis inter cives, et belli 
contra adversarios. Et quoniam hujusmodi leges fuerunt 
datae, quantum potuit humana ratio, ut Aristoteles vult in 
fine Ethicorum^ ubi transit ad librum legum dicens, ' dicamus 
nunc quantum possibile est philosophiae in rebus humanis/ &c. 
principes mundi noluerunt recipere legem Christi, quae fuit 
supra humanam rationem, et ipsi fuerunt regulati secundum 
philosophos, et ideo philosophia impedivit ingressum fidei, et 
tardavit in hoc, quod mundus ea deductus legi celsiori horruit 
consentire. 

Caeterum non solum hoc modo philosophia tardavit fidem 
Christi, sed jure legum suarum de reipublicae defensione ab 
omni contrario sensu visa est per judicia futurorum et 
ostensionem rerum occultarum praesentium, et per opera 
mirabilia supra naturae et artis communiter operantium 
potestatem, contendere cum fidei praedicatoribus, quorum 
proprium fuit non per naturam et artem, sed per Dei virtutem, 
prophetiam de futuris eructare, occulta producere in lucem, 
miracula suscitare. Nam quod philosophiae potestas valeat 
magnifica peragere, quae vulgus non solum laicorum sed etiam 
clericorum duceret pro miraculis, sequentia declarabunt. 
Necnon rectores rerumpublicarum ubique per consilia philo- 
sophorum suas leges zelantium persecutionis et mortis judicia 
sanctis Dei graviter intulerunt. Insuper ars magica per totum 
orbem invalescens, occupans homines in omni superstitione et 
fraude religionis, quamvis fuerat philosophis odiosa, et ab 
omnibus debellata, ut certificabitur suo loco, tamen sancti 
primitivi invenientes mundum occupatum in utraque pro 
eodem artificio utramque reputabant, quoniam ambae fidei 
fructum impediebant multis modis. Nam sicut magi Pharaonis 
Moysi resistebant et populum Aegypti mandato Dei in- 
obedientem faciebant, sic fuit in principio ecclesiae per artis 
magicae violentiam. Quae cum in eundem effectum, scilicet 
contra opus fidei, cum philosophia concordabat, totum ejus 
vituperium in philosophiam redundabat. 

Praeterea Deo placuit a principio ecclesiae quod nullum testi- 
monium humanum ei daretur, sed ut veritas fidei tanto vigore 



30 OPERIS MAJORIS PARS PRIMA. 

mundoradiaret, ut probaretur solum Deo auctore promulgari 
per testes ab ejus imperio destinatos. His igitur de causis 
philosophia fuit ab ecclesia m principio et sanctis Dei non 
solum neglecta, sed eis odiosa ; non tamen propter aliquod quod 
in ea continetur contrarium veritati. Nam licet imperfecta sit 
respectu professionis Christianae, tamen ejus potestas non est 
sectae Christi dissona, immo totaliter ad eam disposita, et 
ei utilissima et omnino necessaria, sicut omnes credunt, et 
certificabitur evidenter. Non igitur propter aliquid malum 
philosophiae ecclesia Dei neglexit et reprobavit eam a prin- 
cipio, sed propter abusores ejus, qui noluerunt eam suo fini, 
qui est veritas Christiana, copulare. Et propter hanc causam 
Ecclesia primitiva non fuit soHicita de translatione magnarum 
scientiarum philosophiae, et ideo sancti doctores Latini copiam 
philosophicorum non habent, et configurantes se principiis 
Ecclesiae neglexerunt multa dignissima, sicut in principio 
propter causas supradictas neglecta fuerunt, non propter 
aliquid falsum vel indignum quod in philosophia reperiri 
possit, ut certius suo loco per ipsos Dei sanctos patebit. Nam 
ostendetur quod sancti Patriarchae et Prophetae a principio 
mundi omnes scientias receperunt a Deo, quibus illam magnam 
vitae longitudinem dedit, ut possent experiri quid eis fuerat 
revelatum, quatenus, fide Christi introducta et evacuata artis 
magicae fraudulentia, potestas philosophiae ad divina utiliter 
rapiatur. 

Capitulum XV. 
The ex- Sicut vero doctores sacri magnificas scientias philosophiae 

ample not , , . , . ... *^ . 

to bc fol- non habuerunt in usu, sic nec postenores, scincet Gratianus, 
later Ih^^ Magistcr sententiarum ct historiarum, Hugo de Sancto Victore, 
logians. et Ricardus de eodem. Nam non fuerunt corum temporibus 
translatae, nec in usu Latinorum, et ideo neglexerunt eas, nec 
dignas sacris mysteriis sciverunt judicarc, sed humano sensu 
rcspuebant quorum usum non habcbant, ct in multis oblo- 
quuntur, sumentes nihilominus occasionem ex hoc, quod 
sancti doctores prius easdem ncglexerunt ; sed non attcnde- 
bant causas sanctorum, scilicct, quod non sunt translatae in 
eorum tcmpore, et etiam quia ecclesia eas jubere transfcrri 



CAUSAE ERRORIS. 31 

propter causas quinque prius tactas neglexit. Moderni vero 
doctores vulgi, licet multa de philosophia sint translata, tamen 
non habent eorum usum, cum et in parvis et vilibus delectati 
duos libros logicae meliores neghgunt, quorum unus translatus 
est cum commentario Alpharabii ^ super illum, et alterius ex- 
positio per Averroem facta sine textu Aristotelis est translata. 
Et longe magis caetera, quac minorem obtinent dignitatem, 
sicut novem scientias mathematicae, et sex scientias magnas 
naturales, quae multas alias scientias sub se comprehendunt, 
atque morales quatuor partes negligunt dignissimas ; et suae 
ignorantiae quaerunt miserabile solatium per Gratianum et 
caeteros magistros authenticos, qui non habuerunt notitiam 
partium philosophiae. Nam post Christum sancti non sunt 
usi dignitate philosophiae, at non propter hoc, quod ipsa sit 
sacris contraria sententiis vel indigna, cum ad theologica 
absolute intelligenda, et respectu ecclesiae Dei et reipublicae 
fidelium ac conversionis infidelium utiliter et magnifice possit 
adjuvare, sicut certificabitur suo tempore. Et tanto misera- 
bilius est quod multitudo studentium modernorum magnas 
negligit scientias, cum tamen fuerunt introductae post 
Gratianum. Aliqui adhuc vivunt qui in studiis eas per- 
l^erunt. 

Capitulum XVI. 

Quamvis autem istas causas malorum omnium universales No sudden 
persecutus sum, et vellem omnia reduci ad auctoritatem ^Sl^^for. 
solidam, et sensum sapientum et expertorum, qui pauci sunt, Kefonn 
non tamen credat Serenitas Vestra, quod ego intendo Vestriae.in the 
clementiam Sanctitatis excitare, ut auctores fragiles et ipsam ^J|^«st 
multitudinem Majestas Papalis violenter invadat; nec quod 
ego indignus sub umbra Gloriae Vestrae suscitem aliquam 
super facto studii molestiam ; sed ut mensa Domini fercuhs 
sapientalibus cumulata, ego pauperculus micas mihi colligam 
decidentes. Poterit enim Vestrae Potentiae magnitudo sibi et 
successoribus suis providere de totius sapientiae compendiosa 
plenitudine non solum absolute habenda, sed quatuor modis 

' See note to p. 100. 



32 OPERIS MAJORIS PARS PRIMA, 

praedictis comparata. Deinde cum Vcstrae Paternitatis dis- 
cretio planiorem de his certitudinem reportaverit, poterit 
auctoritatis vestrae judicium studiosis et sapientibus de facili 
persuadere, ut quod vulgus studentium capere non potest, 
cupidi sapientiae se gaudeant obtinere; insuper quantum 
sufficit multitudini spes promittit. Nam Hieronymus dicit 
super Isaiam, ' Multitudo, accepta veritate, de facili mutat 
sententiam.* Et hoc verum est nisi quando captiosis malesanis 
retractatur. Nam licet vulgus de se sit proclive ad malum, et 
quia saepius invenitur caput languidum, tamen nisi qui praesit 
impediat, satis facile est ad bonum imperfectum, quia instabih*s 
est, et semel mota modum servare non potest, et ideo de facili 
quantum est de se vertitur ad contraria secundum regimen 
praesidentis ; quoniam omni vento doctrinae flectitur, velut 
arundo, et quod principi ejus placet legis habet vigorem. Nos 
enim hoc videmus in omni congregatione hominum, quod 
secundum arbitrium capitis membra moventur. Nam si qui 
praeest bonum negligit, subditi obdormiunt; si ad malum 
excitati, in idem currunt cum furore ; si ad bonum, similiter 
sine discretione festinant. Et si vias perfectionis monet ^ tunc 
olfacit a longe multitudo, sed gustare non potest nec ab ea 
debet requiri, ut superius ostensum est. Quod si non est 
temporis vestri omnia apud vulgum consummare ; poterit 
Vestra Magnificentia locare fundamenta, fontes eruere, radices 
figere, ut Vestrae Sanctitatis successores quod feliciter in- 
ceptum fuerit valeant faciUus adimplere. 

* movet, J. 



PARS SECUNDA 

HUJUS PERSUASIONIS. 
Capitulum I. 

Relegatis igitur quatuor causis totius ignorantiae humanae Theology 
generalibus,volo in hac secunda distinctione unam sapientiam trcs»- 
esse perfectam ostendere, et hanc in sacris literis contineri ; «cience. 
de cujus radicibus omnis veritas eruitur. Dico igitur, quod est 
una scientia dominatrix aliarum, ut theologia, cui reliquae 
penitus sunt necessariae, et sine quibus ad effectum pervenire 
non potest ; virtutem in suum jus vindicat, ad cujus nutum 
et imperium caeterae jacent ; una tamen est sapientia per- 
fecta, quae in sacra scriptura totaliter continetur, per jus 
canonicum et philosophiam explicanda, et expositio veritatis 
divinae per illas scientias habetur. Nam ipsa cum eis velut 
in palmam explicatur, et tamen totam sapientiam in pugnum 
colligit per seipsum. Quoniam ab uno Deo data est tota 
sapientia et uni mundo, et propter unum finem. Quapropter 
haec sapientia ex sua triplici comparatione unitatem sortietur. 
Caeterum via salutis una licet gradus multi ; sed sapientia 
est via in salutem. Omnis enim consideratio hominis, quae 
non est salutaris, est plena caecitate, et ad finalem inferni 
deducit caliginem ; propter quod multi sapientes famosi ^ 
damnati sunt, quia veram sapientiam non habuerunt, sed 

^ In his conimentary on the Secreium Seariorum, Bacon, alluding to the 
legend that Aristotle ascended to heaven in a column of fire, remarks : ' Haec 
est sententia philosophonim paganonim. Sed nobis Christianis non est licitum 
hoc sentire nec finnare; quod nisi habuisset fidem Christi revelatam ei, ac 
fuisset instnictus a prophetis, salvari non potuit Nescimus tamen quod Deus 
fecit ei et aliis dignis prophetis et philosophis quibus dedit magnalia sapientiae.* 
[Tanner MSS. ii6, Sec. Secret. cap. i.] 
VOL. L D 



34 OPERJS MAJORIS PARS SECUNDA. 

apparentem et falsam, unde se aestimantes sapientes stulti 
facti sunt secundum scripturam. Augustinus loquens de sacra 
scriptura dicit libro secundo de doctrina Christiana, ' si verum 
est, hic invenitur; si contrarium, damnatur/ Et vult quod 
ubicunque invenerit Christianus, Domini sui intelligat veritatem 
esse. Veritas Jesu Christi est sapientia sacrae scripturae. 
Ergo non alibi veritas est, nisi quae in illa continetur scientia. 
Et Ambrosius super epistolam ad Colossenses dicit, * Omnis 
ratio supemae scientiae et terrenae creaturae in eo est, qui 
est caput et auctor, ut qui hunc novit, nihil ultra quaerat, 
quia hic est perfecta virtus et sapientia. Quicquid alibi 
quaeritur, hic perfecte invenitur/ Cum ei^o sacra scriptura 
dat nobis hanc sapientiam, manifestum est quod hic omnis 
veritas sit conclusa ; si aliqua est sapientia huic contraria, erit 
erronea, nec habebit nisi nomen sapientiae ; sed diversitas. 
quam non faciat alibi, contrarietatem hic tamen inducit, sicut 
patet per evangelicam auctoritatem, *Qui non est mecum, 
contra me est' Sic de hac sapientia verum est, ut quod illi 
annexum non est contra illam esse probetur, et ideo Christiano 
abhorrendum. 



Capitulum II. 

Intheology Haec autem manifestius patent consideranti divisionem 

(inclndil^ scientianim. Nam si nitamur separare scientias ab invicem, 

the Canon non possumus dicere theologiam. Sub una enim parte philo- 

rooted. sophiae, scilicet morali quam Aristoteles civilem nominavit, 

continetur jus civile, ut inferius innotescet. Canonicum ^ vero 

jus a scripturis sacris nominatur, non ab aliis, sicut ip^um 

nomen demonstrat ; quae scripturae canonicae dicuntur Ubri 

Veteris Testamenti, sicut Decretorum parte prima distinctione 

' The first text-book on Canon Law was the Decretum of Gratian, a monk of 
Bologna, completed probably in 1143. In 1234 Gregory IX pablished five 
books of Decretals, to which a sixth book was subsequently added by Boniface 
at the end of the century. Bacon, giving way to the strong prejudice felt by 
himself and other theologians against the Civil Law, maintains that the Canon 
Law is founded in the main on Scripture. But in reality the Canon Law is based 
on the Civil Law. ' Eveiything in the Canon Law was Roman which was not of 
direcUy Christiaii or Jewish origin.' (Rashdall, Mtdkuvai UMwersUies^ i. p. 133.) 



PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 35 

nona habetur, aut canones nuncupantur. Nam Canan Graece, 
Regula Latine dicitur. Et tam jus canonicum quam jus 
divinum regularem modum vivendi reddere comprobatur. 
Caeterum jus canonicum totaliter fundatur super auctoritate 
scripturae et expositore. Nam aut pro constitutionibus alle- 
gantur auctores sacrae scripturae, ut Augustinus et alii, aut 
summi pontifices pro suis statutis indicant auctoritates et 
exempla Novi et Veteris Testamenti ; et ideo hoc jus non 
est nisi explicatio voluntatis Dei in scriptura. Item jus 
canonicum vocatur ecclesiasticum, quo regitur in spiritualibus 
Dei ecclesia, tam in capite quam in membris. Sed nihil 
aliud sonat scriptura nisi hoc regimen. Praeterea jus naturale 
continetur in sacra scriptura sicut docetur in principio decreti 
manifeste. Jura canonica non possunt esse aliena a jure 
divino, imo de fontibus illius debent derivari, et jus commune 
est divinum vel humanum ; divinum est quod spiritu Dei 
allatum est mundo in sua scriptura ; humanum quando sensu 
hominis est adinventum. Sed constat ecclesiam Dei rcgi jure 
canonico. Quapropter idem jus est divinum, de thesauro 
sacrae scripturae eruendum. Et hoc manifestum est con- 
sideranti partes juris canonici. Nam vel ordinat gradus 
ecclesiasticorum oflficiorum, vel sacra Dei determinat, vel 
forum conscientiae discutit, vel causas ecclesiasticas discindit. 
Sed horum omnium radices et ipsa stipes erecta apud sacram 
scripturam reperiuntur. Rami vero penes expositores ejusdem, 
ut in canone folia, flores, fructus salutiferi capiantur. Nam 
sermones canonici suavis omatus foliis comparantur secundum 
scripturam. Flores autem et fructus sunt segetum aurei 
palmites et uvarum maturitio. Et ideo jus canonicum sine 
potestate scripturae in uno corpore continetur, sicut unius 
arboris corpus ex radicibus et stipite, ramis, floribus, et fruc- 
tibus constituitur. 

Capitulum III. 

Quod autem philosophia ^ non sit aliena a Dei sapientia, sed ^t. Au- 
in ipsa conclusa, manifestandum est. Si enim a philosophis maintained 

^ philosophiae, J. 
D 2 



36 OPERIS MAJORIS PARS SECUNDA. 

that theo- tanquam injustis possessoribus rapere debent Christiani utilia 
dudeT" ^"^^ ^^ libris eorum continentur, sicut dicit Augustinus, patet 
philosophy. quod philosophia est condigna sacrae veritati. Et iterum in 
libro, scilicet de doctrina Christi, dicit quod philosophoruni 
aurum et argentum non ipsi instituerunt, sed de communibus 
quasi metallis divinae providentiae, quae ubique est effusa, 
eruitur; quod praefiguratum fuisse dicit, sicut Aegyptii 
fecerant vasa atque ornamenta de auro vel argento et vestem 
quam ille populus exiens de Aegypto sibi potius tanquam ad 
usum meliorem vindicavit, sic doctrinae gentilium liberales 
disciplinas usui veritatis aptiores et morum praecepta utilis- 
sima continent, deque Deo ipso colendo multa inveniuntur 
apud eos. Ulterius hoc explicat, dicens, in omnibus humanis 
tractatibus, quae sunt moralia, vel historialia vel artificialia, 
naturalia, logicalia vel grammaticalia, sunt nobis necessaria. 
Nam pro moralibus dicit vestem, quae illorum est hominum 
quidem institutio sed tamen accommodata humanae societati 
qua in hac vita carere non possumus, in usum converti 
christianum debet. De historialibus dicit, historia gentilium 
plurimum nos adjuvat ad sanctos libros intelligendos. De 
aliis vero considerationibus tam artificialibus quam naturalibus 
dicit, Artium autem cacterarum, quibus adfabricatur domus,et 
hujusmodi, medicinae, vel agriculturae, vel quorum omnis 
effectusactio est, ut saltationum, cursionum, &c., harum autem 
cognitio usurpanda est ad judicandum, ne omnino nesciamus 
quid scriptura velit insinuare, cum de his artibus aliquas facit 
figuras. Pro omnibus naturalibus dicit, Benignam sane 
operam faceret pro sacra scriptura, qui proprietates temporum 
et locorum, lapidum, et caeterarum rerum inanimatarum, 
plantarum et animalium colligeret. Et pro logicalibus dicit, 
Nam de eis pro theologia possunt quaedam necessaria colligi 
et condigna, sed non video, ut ait, utrum hoc possit sine eis. 
Atque in libro secundo de ordine disciplinae dicit, Ad sacram 
scientiam nuUus debet accedere sine scientia logicali. De 
mathematicis dicit Cassiodorus, Geometriam, arithmeticam, 
astronomiam, musicam cum sollicita mente revolvimus, sensum 
acuunt, limamque ignorantiae detergunt, et ad illam divinam 
contemplationem, Deo largiente, perducunt ; quas merito 



PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 37 

sancti patres legendas persuadent, quoniam ex magna parte 
appetitus a camalibus rebus extrahitur, et faciunt desiderare 
quae solo corde possumus respicere. Et Augustinus doctos 
multos sanctos fuisse commemorat, cum quaerit, Nonne aspi- 
cimus quanto auro subsarcinatus exierit de Aegypto Cyprianus 
doctor suavissimus et martyr beatissimus, quanto Victorinus et 
alii multi innumerabiles Graeci, et Moyses quidem eruditus 
omni sapientia Aegyptiorum ? 



Capitulum IV. 

Non solum autem beatus Augustinus, sed et alii sancti Corrobora- 
idem asserunt, Nam Hieronymus ad magnum oratorem other^^ 
dicit, Si scripturas sacras legeres, quis nesciat et in Moyse ac auihonties. 
prophetarum libris quaedam assumpta ex gentilium h'bris? 
Et inducit ad hujus probationem prophetas ipsos et omnes 
doctores famosos a principio ecclesiae, qui philosophorum 
doctrinis fidem Christi persuaserunt principibus ct infidelibus, 
ac roboraverunt multipliciter. Et Beda super librum Regum 
dicit, quod liberalium scientiarum sapientiam quasi suam 
sumere licitum est Christianis ac divinam, ah'oquin Moysen et 
Daniel sapientia Aegyptiorum et Chaldaeorum non paterentur 
erudiri. Iterum de factura templi dicit Solomonem cum suis 
servis signare Christum, et Hiram cum suis significare philo- 
sophos et sapientes gentiles, ut templum Dei, hoc est ecclesia, 
non solum sapientia apostolica, sed philosophorum con- 
strueretur ; quia gentiles ab errore conversi atque ad veritatem 
evangelii transformati, melius ipsos gentium errores noverant, 
et quo certius noverunt, eo artificiosius hos expugnare atque 
evacuare didicerunt. Paulus evangelium quod per revela- 
tionem didicerat, melius novit ; sed Dionysius melius revincere 
poterat falsa dogmata, quorum cum erroribus argumenta 
a puero noverat ; et ideo Salomon dicit, Scis enim quod non 
est in populo meo vir, qui noverat ligna caedere, sicut Sidonii. 
Haec et hujusmodi multa allegat venerabilis Beda. Sed et 
Paulus Apostolus Epimenidis poetae usus est versiculo, 
scribens ad Titum, *Cretenses semper mendaces, malae 



38 OPERIS MAJORIS PARS SECUNDA, 

bestiae, ventres pigri/ la alia quoque epistola Menandri 
ponit senarium, * Corrumpunt bonos mores confabulationes 
pessimae.' 

Capitulum V. 

Thcprin- Causae autem, quare sancti affirmant quod quaerimus, et 

stire^our*^ figuratum fuisse declarant, possunt assignari ; primo propter 

intellectual hoc quod ubicunque veritas invenitur, Christi judicatur se- 

wthout us, cundum sententias et auctoritates superius allegatas. Idcirco 

not within. quamvis aliquo modo veritas philosophiae dicatur esse eorum ; 

ad hanc tamen habendam primo lux divina influxit in animos 

eorum, et eosdem superillustravit ; * IUuminat enim omnem 

hominem venientem in hunc mundum,* sicut dicit scriptura ; 

cui sententiae philosophi ipsi concordant. Nam ponunt in- 

tellectum agentem et possibilem ^ ; anima vero humana dicitur 

ab eis possibilis, quia de se est impotens ad scientias et 

virtutes, et eas recipit aliunde. Intellectus agens dicitur, qui 

^ This passage deals with one of the most important of mediaeval contro- 
versies in which Aquinas was at issue with Averroes and his Arabian pre* 
decessors. These maintained the existence of an universal reason, of which 
individuals were more or less the partakers. Aquinas refutes this view in 
.S. T., Pars i, Quaest. Ixxvi. Art. a: 'Utrum intellectivum principium multipli- 
cetur secundum multiplicationem corporum.' See also his systematic treatise, 
De Umiate Initlfectus. It will be seen that Bacon in this passage appears to 
side with the Arabians against St. Thomas. Cf. also the corresponding passage 
in Opus Teriium, cap. 93. But in his more elaborate treatment of the subject in 
Communia Naiuralium (unpublished), Pars iv. cap. 14, he is careful to distin- 
guish his doctrine from that of Averroes. That there should be a divine light 
pervading the world, was one thing : that the intellect of mankind should be 
one and the same substance, was quite another thesis which cut at the root 
of morality. Renan (Averroes, p. 71 et seq.) shows that, though the doctrine 
altacked by St. Thomas is commonly identified with Averroes, it had been 
held by Aikindi, Alfarabi, and Avicenna centuries before. It may be noted, 
in passing, that Jebb's error in writing repeatcdly inierius for iniellectus has 
gone far to make this passage unintelligible. 

AristoUe can hardly be called as a witness for the Arabian side of the contro- 
versy, though his distinction between intellect and the other physical facul- 
ties is of course emphatic enough. Cf. De Anima, iiL 4, $ 5 rb /4v ydp 
alffOfiTiKdy oifK avtv oiffMTOSf 6 8« {povs) x^P^^^^» Again, ii. a, $ 9 tovto i»&¥0¥ 
|y8<x<ra< X^f^i^^^i tccu$dv€p t6 dttkop rov ipSaprov. The passage of the transla- 
tion of which Bacon complains is De Anima, iii. 5 kvtl 5' Acrircp kw Av6.a}f rg 
^vaci ioTi Ti t6 iikv vkq kxdffT^ yiv€i {jovro 8' t vdvra ivpdfui iietiva), trfpov S^ 
t6 atriov xal woiTjructv t^ woitiv wdvra, olov 1} tix^ ^P^^ Tifv HKrfv w4wov$€v f dvdyKii 
Koi h rg ^XV ^opxfiv rat/roff rds dia^pds. 



PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 39 

influit in animas nostras illuminans ad scientiam et virtutem ; 
quia licet intellectus possibilis possit dici agens ab actu intelli- 
gendi, tamen sumendo intellectum agentem ut ipsi sumunt, 
vocatur influens et illuminans possibilem ad cognitionem veri- 
tatis. Et sic intellectus agens secundum majores philosophos 
non est pars animae, sed est substantia intellectiva alia et 
separata per essentiam ab intellectu possibili; et quia istud 
est necessarium ad propositi persuasionem, ut ostendatur quod 
philosophia sit per influentiam divinae illuminationis, volo 
illud efficaciter probare ; praecipue cum magnus error inva- 
serit vulgus in hac parte, necnon multitudinem magnam 
theologorum, quoniam qualis hic est in philosophia, talis in 
theologia esse probatur. Dicit enim Alpharabius in libro de 
intellectu et intellecto, * Quod intellectus agens, quem nomi- 
navit Aristoteles in tertio tractatu suo de anima, non est in 
materia, sed est substantia separata.* Et Avicenna quinto de 
anima et decimo metaphysices idem docet, necnon ipse philo- 
sophus dicit, * Quod intellectus agens est separatus a possibili et 
immixtus.' Item vult quod intellectus agens sit incorruptibilis 
secundum esse et substantiam, quoniam dicit ipsum differre 
a possibili penes incorruptionem, sed possibilis est incorrupti- 
bilis secundum substantiam, et corruptibilis secundum esse, 
propter separationem ejus. Ergo agens secundum esse et 
substantiam erit incorruptibilis ; quapropter non erit pars 
animae, quoniam tunc secundum esse suum in corpore cor- 
rumpetur, quando separetur ; et dicit, quod se habet ad possi- 
bilem, sicut artifex ad materiam, et sicut lux solis ad colores. 
Artifex enim est extra materiam in quam agit, et separatus 
ab ea per essentiam ; similiter lux solis expellens tenebras a cor- 
poribus separata est ab eis per essentiam, et advenit aliunde. 
Dicit etiam, intellectus agens scit omnia et [est] semper 
in actu, quod nec animae nec angelo convenit, sed soli Deo ; 
item a digniore parte magis habet res denominari, ergo magis 
dicetur sciens per agentem, quam ignorans per possibilem, 
ante inventionem et doctrinam. Item Aristoteles ^ dicit quod 

^ Aristotle puts forward this view tentatively before he had come to a definite 
conclusion as to the distinction between reason and other faculties. DeAnima, 
ii. I, § xa '^Ad^XoK «i oStrw kvrtKix^^ia rov ir^t/mTot 4 ^xi Swwp vkanilp wKoiov, 



40 OPERIS MAJORIS PARS SECUNDA. 

intellectus est in corpore, sicut nauta in navi quantum ad hoc, 
quod non est alligatus alicui parti, sicut nec nauta navi ; sed 
nauta non est profectio, sed motor tantum. 

Cum igitur haec sententia sit consona veritati, ut textus phiio- 
sophi evidenter praetendit, et expositores declarant, ne aliquis 
cavillator a latere insurgat, allegans idem quo vulgus decipitur, 
dico quod Aristoteli imponuntur ista verba, * Quoniam in omni 
natura est aliquid quod agat et aliud quod patiatur, ista est in 
anima/ immo respondeo quod multoties falso translatum est 
et obscurum. Nam cum tertio caeli et mundi dicatur, quod 
circulus et figura orbicularis replent locum ^, istud est falsum ; 
ut sciunt experti in naturalibus et geometricis, sicut Averroes 
demonstrat ibidem. Et quod tertio Meteorologicorum dicitur 
de iride est falsum etiam. Nam experientia docet, quod 
quandocunque luna sit plena et pluat, nec ipsa sit nubibus 
cooperta, accidit iris. Et sunt multa alia falso translata,cujus 
causa patebit ex tertia parte hujus operis, et plura obscura, in 
quibus quilibet alii potest contradicere. Et in hoc loco accidit 
utrumque vitium vcl saltem secundum, quod probo per ipsum 
Aristotelem. Nam ipse dicit secundo physicorum, quod 
materia non coincidit cum aliis causis in^ eodem secundum 
numerum, ergo in nuUa natura sunt simul agens et materia, 
igitur nec in anima. Si igitur ad literam teneatur textus 
male translatus, tunc omnino falsus est et contra Aristotelem 
alibi, et contradicit sibi tantus auctor; et qualitercunque 
contingat verbum suum in secundo Physicorum est verum, et 
ab omnibus concessum ; ergo sermo suus tertio de anima est 
falso translatus, et indiget expositione. Nam nihil aliud in- 
tendit, nisi quod in anima, videlicet, in operatione requiruntur 
duo, scilicet, agens et materia ; sicut in omni natura, id est 
operatione naturae duo exiguntur, scilicet efficiens et materia. 
Et idem est verum, sed agens semper est aliud a materia et extra 

* In De Caelo, iii. 8, § i, Aristotle distinctly says that only three plane figures 
can form a continuous surface, the triangle, square, and hezagon ; and only two 
soiid figures can occupy space, the pyramid and cube. 

The reference to the lunar rainbow is Meieor. iii. a, § 9. It fully bears out 
Bacon*s view as to fiiulty translation. What AristoUe really said was that 
during an ezperience of fifty years he had only twice observed the lunar 
rainbow. 

* sic, O. cum eodem, J. 



PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 41 

eam secundum substantiam, licet operetur in ea, Caeterum pos- 
sumus aliter hunc locum consolari. Nam Aristoteles quarto^ 
Physicorum dicit, quod octo modi sunt essendi in actu, quorum 
unus est ut movens in moto, quia movens seu agens est se- 
cundum virtutem suam in materia sua, licet non secundum 
substantiam. Et sic est in omni natura in qua operatur, et ita 
in anima ; et sic nullo modo sequitur quod intellectus agens 
sit pars animae, ut vulgus fingit ; et haec sententia est tota 
fidelis et a sanctis coniirmata. Et Augustinus dicit in solilo- 
quiis et alibi, ^Quod soli Deo est anima rationalis subjecta 
in illuminationibus et influentiis omnibus principalibus.' £t 
quamvis angeli purgent mentes nostras et illuminent et ex- 
citent multis modis, et sunt ad animas nostras tanquam stellae 
respectu oculi corporalis^ tamen Augustinus ascribat Deo 
influentiam principalem; soli influentia luminis cadentis per 
fenestram ascribitur, et angelus aperienti fenestram compara- 
tur, secundum Augustinum. Et quod plus est, vult in pluribus 
locis quod non cognoscimus aliquam veritatem nisi in veritate 
increata et in regulis aetemis. Cum Igitur Deus illuminaverit 
animas eorum in percipiendis veritatibus philosophiae, mani- 
festum est quod eorum labor non est alienus a sapientia 
divina. 



Capitulum VI. 

Tertia causa, propter quam sapientia philosophiae reducitur Philosophy 
ad divinam, est quia non solum mentes eorum illustravit Deus {io*'^^'^ * 
ad notitiam sapientiae adquirendam, sed ab eo ipsam habue- 
runt et eam illis revelavit. Et Augustinus dicit super Johan- 
nem, eis praestitit Deus sapientiam. Aristoteles in libro 
secretorum asserit manifeste totam philosophiam fuisse a Deo 
datam et revelatam ; et unus de maximis philosophis, scilicet 
Tullius in quaestionibus Tusculanis quaerit, * Philosophia quid 
est nisi donum, ut ego credo, inventum Dei?' Unde et dicit, 
* quod nec poeta grave plenumque carmen sine coelesti aliquo 
instinctu effundit.* Et Augustinus octavo de Civitate Dei 
docet et approbat quod Socrates pater philosophorum firma- 

> Nat. Ausculi. iv. 3, i i. 



42 OPERIS MAJORIS PARS SECUNDA. 

vit, quod non potesthomo causas rerum scire, nisi in luce 
divina, et per donum ejus. Et quilibet potest per se experiri 
quod nihil primo ab homine invenitur quod sit de potestate 
philosophiae. Et pono de minimo exemplum ; quoniam licet 
universah'a Porphyrii sunt apud eum sufficienter explicata 
per logicam, metaphysicam, et naturalem philosophiam suffi- 
cientissime expositam, tamen non est homo ita bene studiosus, 
quin oportet ut doctores habeat et per longa tempora audiat 
et studeat, antequam sciat totam veritatem universalium. Et 
nullus vix ante mortem cognoscit ; quod patet propter dis- 
cordiam omnium ^ quia aliqui ponunt ea solum in anima, 
aliqui extra, aliqui medio modo. Si igitur talis ignorantia 
est horum, multo magis per se nunquam perveniet homo ad 
veritatem philosophorum. Quapropter veritatem horum est 
necesse a principio fuisse homini revelatam. Et cum puerilis 
revelatio est necessaria, multo fortius in tota sapientia philo- 
sophiae, quod et a Deo est, et ille dedit et revelavit, et ideo 
oportet quod suae sapientiae sit conformis. 



Capitulum VII. 

neededfor Caeterum totius philosophiae decursus, consistit in eo, ut 
t e ac^uisi- pgj. cognitionem suae creaturae cognoscatur creator, cui propter 



truth. 



tion of 

divine reverentiam majestatis et beneficium creationis et conserva- 
tionis et futurae felicitatis serviatur in cultu honorifico et 
morum pulchritudine et legum utilium honestate; ut in pace 
et honestate vivant homines in hac vita. Philosophia enim 
speculativa decurrit usque ad cognitionem creatoris per 
creaturas. Et morah*s philosophia morum honestatem, leges 
justas, et cultum Dei statuit, et persuadet de futura felicitatc 
utiliter et magnifice secundum quod possibile est philosophiae. 
Haec sunt ccrta discurrentibus per omnes partes philosophiae 

^ Bacon*s attitude in the controversy on Universals is not easy to define 
with precision. ^ Universaie,' he says {Communia Naiuralium), * non est nisi 
convenientia plurium individuorum.* The universal anU rem he entirely rejected. 
' Individuum est prius secundum naturam.' See Charles*s monograph, pp. 339 
and 383-9. A property or attribute common to several individuals (' natura aliqua 
communis solis individuis ') would seem to be his definition of it. But Bacon 
attached less importance to the controversy than his contemporaries. 



PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 43 

principales, sicut sequentia docebunt. Cum igitur haec sint 
omnino necessaria christianis, et omnino consona sapientiae 
Dei, manifestum est quod philosophia necessaria est legi 
divinae et fidelibus in ea gloriantibus. 



Capitulum VIII. 

Item omnes sancti et sapientes antiqui in suis expositionibus Spiritual 
sensum literalem coUigunt ex naturis rerum et proprietatibus ^^derlies 
earum, ut per convenientes adaptationes et similitudines phyaical. 
eliciant spirituales sensus : quod declarat Augustinus libro de 
doctrina Christi secundo, ponens exemplum de verbo Domini 
dicentis, * Estote prudentes sicut serpentes, et simplices sicut 
columbae.* Nam voluit Dominus per hoc, ut ad similitudinem 
serpentis totum corpus exponentis pro defensione apostoli et 
apostolici viri se et sua darent pro Christo capite suo et pro 
fide sua. Et propter hoc omnis creatura in se vel in suo 
simili, vel in universali vel in particulari, a summis coelorum 
usque ad terminos eorum ponitur in scriptura, ut sicut Deus 
fecit creaturas et scripturam, sic voluit ipsas res factas ponere 
in scriptura ad intellectum ipsius tam sensus literalis quam 
spiritualis. Sed tota philosophiae intentio non est nisi rerum 
naturas et proprietates evolvere, quapropter totius philosophiae 
potestas in sacris literis continetur; et hoc maxime patet, 
quia longe certius ac melius et verius accipit scriptura 
creaturas, quam labor philosophicus sciat eruere. Quod pro 
infinitis exemplis pateat ad praesens in Iride. Philosophus 
Aristoteles suis obscuritatibus nos perturbat ut nec aliquid 
quod dignum sit valeamus per eum intelligere. Nec mirum, 
cum Avicenna dux et princeps philosophiae fateatur se 
naturam Iridis ignorasse ; et causa hujus est, quia philosophi 
causam Iridis finalem ignoraverunt ; et ignorato fine ignorantur 
ea quae sunt ad finem ; quia finis imponit necessitatem iis 
quae ad finem ordinantur, ut Aristoteles vult secundo Physi- 
corum. Causa vero finalis Iridis est dissipatio humiditatis 
aqueae, sicut patet ex libro Geneseos; unde semper in 
apparitione Iridis est nubium resolutio in stillicidia infinita, ut 
consumantur aqueae humiditates tam in aere, quam in mari 



44 OPERIS MAJORIS PARS SECUNDA. 

et terra, quia una pars Iridis cadit in sphaeras aquae et terrae. 
Consumptio vero aquae non potest esse per Iridem, nisi 
propter radios soHs facientis eam. Nam per varias reflec- 
tiones et fractiones congregantur radii infiniti, et congregatio 
radiorum est causa resolutionis et consumptionis aquarum, et 
ideo Iris generatur per reflectiones multipHces. Non enim 
possunt radii congregari, nisi per fractionem et reflectionem, 
ut postea patebit. Ex scriptura igitur Geneseos cum dicitur 
'Ponam arcum meum in nubibus coeli, ut non sit amplius 
diluvium super terram,' accipitur causa finalis ipsius Iridis. 
Ex quo investigari potest causa efficiens, et modus generandi 
Iridem, qui modus non fuit notus philosophis sufficienter 
secundum quod libri eorum manifestant nobis. Et ita est de 
omni creatura. Impossibile enim est quod homo sciret 
veritatem creaturae ultimam secundum quam accipitur in 
scriptura, nisi fuerit specialiter a Deo illustratus. Nam 
creaturae accipiuntur ibi propter veritates gratiae et gloriae 
eliciendas, quas philosophi nescierunt, et ideo ad potestatem 
ultimam sapientiae creaturaruni non venerunt, sicut sacra 
scriptura eam in suis continet visceribus. Unde tota philo- 
sophia jacet in sensu literali sacris mysteriis gratiae et gloriae 
decorata, tamquam quibusdam picturis etcoloribus nobilissimis 
redimita. 

Capitulum IX. 

rhiiosophy Distinctio finah*s^ hujus partis, in qua ad confirmationem 
loThc*^ omnium praedictorum et dicendorum ostenditur quod tota 
patriarchs. sapientia revelata est primo sanctis ; et ostenditur propositum 
in universali. 

Et hoc ultimo confirmari potest per hoc, quod eisdem 
personis data est philosophiae plenitudo quibus et lex Dei, 
scilicet, sanctis patriarchis et prophetis a principio mundi, 
Et non solum est necessarium propter articulum qui hic trac- 

^ In the MSS. this is called Distinctio tertia, but as no first and second 
Distinctions are noted, I have subsiituted the word * finalis.' This concluding: 
portion of Part II, which is of great importance, seems to have been added 
by Bacon as an appendix. The MS. has no division into chapters; I bave 
supplied this. 



PHILOSOPHIAE CUM THEOLOGIA AFFINITAS, 45 

tatur, sed propter totum negotium sapientiae certificandum. 
Nam impossibile fuit homini ad magnalia scientiarum et 
artium devenire per se, scd oportet quod habuerit revelationem, 
qua probata nihil debet apud nos dubitari de arcanis sapientiae 
repertis apud auctores. Sed nullum capitulum sapientiale 
est tanti laboris sicut est certificatio hujus rei, eo quod est 
magnum fundamentum totius comprehensionis humanae. 
Atqui contrarietates et dubia multipliciter intercurrerunt, et 
oportet auctores et volumina abundantius revolvi quam pro 
aliquo alio articulo, qui in toto sapientiae studio valeat 
reperiri. Dico igitur quod eisdem personis a Deo data est 
philosophiae potestas quibus et sacra scriptura, videh'cet, 
sanctis ab initio, ut sic appareat una sapientia esse completa 
et omnibus necessaria. SoH enim patriarchae et prophetae 
fuerunt veri philosophi qui omnia sciverunt, non solum legem 
Dei, sed omnes partes philosophiae. Hoc enim nostra scrip- 
tura satis nobis ostendit, quae Joseph crudivisse principes 
Pharaonis et senes Aegypti prudentiam docet; et Moysen 
fuisse peritum in omni sapientia Aegyptiorum. Et Bezaleel et 
Eliab hoc demonstrant, qui omni intellectu et sapientia rerum 
naturalium fuerunt illustrati ; uno enim flatu Spiritus Sanctus 
eos iiiuminavit et docuit totam potestatem naturae in rebus 
metallicis et caeteris mineralibus Sed et Solomon sapientior 
omnibus praecedentibus et subsequentibus secundum testi- 
monium scripturae plenam obtinuit philosophiae potestatem. 
Et Josephus primo antiquitatum libro, capite secundo, dicit, 
quod cum filii Adae per Seth fuerunt viri religiosi et ab ipso 
Deo dilecti, Deus dedit eis sexcentos annos vivere propter 
gloriosas partes philosophiae in quibus studuerunt, ut, quod 
Deus eis revelavit, possent experiri per vitae longitudinem ; 
et addit, quod Noe et filii ejus docuerunt Chaldaeos partes 
philosophiae, et quod Abraham intravit Aegyptum et 
docuit Aegyptios. Et postea in octavo libro, quod nullam 
naturam inexaminatam Solomon praeteriit, sed de omnibus 
philosophatus est, et disciplinam proprietatum earum evidenter 
exposuit, et tangit quomodo descendens ad singula com- 
posuerit quatuor millia librorum et quinque. 

£t maximus Aristoteles ipsa veritate coactus dicit in libro 



46 OPERIS MAJORIS PARS SECUNDA. 

By thesc secretorum ; * Omnem sapientiam Deus revelavit suis prophetis 
of Greece" ^ justis et quibusdam aliis, quos praeeleg^t et illustravit spiritu 
^<^« *"i" divinae sapientiae, et dotavit eos dotibus scientiae. Ab istis 
enim sequentes philosophi philosophiae principium et originem 
habuerunt et scripserunt artium et scientiarum principia et 
secreta, quia in scriptis eorum nihil falsum nihil reproban- 
dum invenitur, sed a sapientibus approbatum.' Et Averroes 
dicit super partem coeli et mundi, *quod in tempore anti- 
quorum ante Aristotelem et alios philosophos fuit philosophia 
completa, ad cujus completionem Aristoteles suo tempore 
aspirabat.' Et apud Albumazar in majori introductorio et 
alibi, et penes aliquos habetur multipliciter, quod Noe et filii 
ejus multiplicaverunt philosophiam ; et praecipue Sem prae- 
valuit in hac parte. Deinde post istos fuerunt viri ^ . . . nomine 
vulgato. Omnes philosophi et poetae majores et juniores 
fuerunt post Noe et filios suos, et Abraham. Nam et Aristo- 
teles et omnes consentiunt in hoc, quod primi philosophantes ^ 
fuerunt Chaldaei et Aegyptii, unde adhaeret sententiis patrum 
Chaldaeorum in undecimo Metaphysicae. Quia licet Noe et 
filii ejus docuerunt Chaldaeos, antequam Abraham docuit 
Aegyptios, tamen non fuit studium more scholastico ita cito 
institutum, sed paulatim crevit ordo ejus et exercitium. 

Quatenus omnis igitur dubitatio toUatur in hac parte, vide- 
amus decursum et seriem infidelium philosophorum, et poeta- 
rum, et omnium soUicitantium de studio sapientiali, et per- 
cipiemus quod post Abraham et decessores suos, quibus a Deo 
sapientia revelata est, inventi sunt singuli qui aliquem titulum 
adepti sunt. Nam quantumcunque volumus strictius compu- 
tare Zoroastres invenit artes Magicas, secundum Augustinum 
vicesimo primo de civitate Dei ; et secundum omnes auctores 
hoc vulgatum est ; sed hic fuit Cham filius Noe, ut Clemens, 
libro suo, et magister historiarum, et speculum historiale con- 
scribunt. Deinde lo, quae postea Isis dicta est, dedit literas 
Aegyptiis, ut Augustinus dicit libro de civitate Dei octavo 

^ There is a hiatus here in O. & D. It may have been supplied by Jul. 
But fire has rendered the passage illegible. 

' There is a reference of this kind in a fragment of an apocryphal work 
attributed to Aristotle entitled Ma^i/r^, quoted by Diog. Latrt, i. z. 



PHILOSOPHIAE CUM THEOLOGIA AFFINITAS, 47 

riecimo. Ante hujus tempora non fuit secundum Augustinum 
sapientiae studium literis et scriptis pertractatum, quamvis 
doctrinis Abraham instructi fuerunt. Et Isis, ut Augustinus 
ait, dicitur fuisse filia Machi, qui fuit primus rex Argivorum, 
qui regnavit primo anno Jacob et Esau nepotum Abrahae, 
sicut Augustinus et historiae confitentur. Quanquam et alii 
voluenint, quod Isis veniret de Aethiopia in Aegyptum, et eis 
literas dedit, et multa beneficia contulit, sicut recitat Augus- 
tinus. Sed tamen ante tempus Machi non fuit, ut in ordine 
regum Aegypti in chronicis reperitur. Eodem tempore fuit 
Minerva aetate virginali apparens, multorum, ut ait Augustinus 
libro praedicto, inventrix, quae Pallas dicitur, et apud poetas 
Dea sapientiae nuncupatur, et Athena vocatur, atque Tritonia, 
ut dicit Augustinus. Et Isidorus hunc locum esse in Africa, 
qui Trito vocatur, recitat octavo libro etymologiarum, et Plinius 
quinto libro, a quo Pallas dicitur Tritonia et fuit temporc 
diluvii Ogygis regis, quod illi ascribitur, quia in Achaia accidit 
tempore ejus, qui secundum Augustinum, Eusebium et Hiero- 
nymum, et Solinum libro de mirabilibus mundi, fuit tempore 
Phoronei filii Machi. Regnavit autem Machus quinquaginta 
annis, et Phoroneus filius ejus sexaginta, cujus tempore facta 
est repromissio Jacob, sicut patri suo, ut dicit Augustinus. Et 
ideo Ogyges fuit tempore Jacob; unde Solinus dicit,diluvium 
primum in Achaia fuisse tempore Ogygis et Jacob patriarchae. 
Quod diluvium fuit ante diluvium Deucalionis per 600 annos, ut 
idem narrat Solinus. Nam ut Hieronymus et Eusebius narrant, 
regnante Cecrope primo rege Atheniensium, sub quo Moyses 
eduxit filios Israel de Aegypto, fuit Deucalionis diluvium. 

Et sub Phoroneo moralis philosophia incepit apud infideles. 
Nam Augustinus dicit, quod sub legum et judiciorum 
institutis Graecia clarior facta est *. Sed post fuerunt mores 
et jura vivendi ; quod patet per inhibitionem sanguinis et 
licentiam de usu camium post diluvium^ et de emptione et 
venditione apud Abraham pro spelunca ; atque ex sanctitate 
Abrahae et patrum suorum I^es honestas et sacras vivendi 
concludit ab eis fuisse edoctos. £t cum minus utiles scientias 
perfecerunt, non debuit tantorum virorum sapientia scientiam 

^ Di CivUaU Dei, lib. xviil cap. 3. 



metheas. 



48 OPERIS MAJORIS PARS SECUNDA. 

morum utilissimam negligere. Deinde primus inter viros 
titulo majoris sapientiae doctor fuisse perhibetur, quia optimus 

Pro- sapientlae investigator fuit, Prometheus *, quem poetae ferunt 

de luto formasse homines, cujus frater, ut dicit Augustinus, 
fuit Atlas magnus astrologus ; unde occasionem, ut Augustinus 
refert, fabula invenit,quod eum portare coelum finxerit,quam- 
vis mons ejus nomine nuncupatur cujus altitudine potius coeli 
portatio vulgo videatur, qui in extremis Africae maritimis 
prope Gades Herculis attollitur velut in caelum. Sed priores 
fuerunt filli Noe et Abraham qui iuerunt periti astronomi, ut 
Josephus narrat et Isidorus tertio libro» et Clemens libro 
primo. Nam hi secundum Augustinum floruerunt, quando 
Moyses natus est. Et Isidorus concordat libro quinto dicens, 
quod Atlas fuit sub servitute filiorum Israel. Atlas vero, ut 
dicit Augustinus, fuit avus maternus Hermetis Mercurii 
majoris, qui magnarum artium peritus floruit et eas hominibus 
tradidit, propter quod eum tanquam Deum post mortem 
venerati sunt. Et hic, ut dicit Augustinus octavo decimo 
librOjfuittempore quo Moyses eduxit filios Israel ; cujus nepos 
fuit Hermes Mercurius, qui ad doctrinam alterius est dictus 
Trismegistus, qui famosus fuit philosophus Aegypti, maxime 
in moralibus, sicut AugustinCls docet octavo de Civitate Dei. 

Aescula- Et hic scripsit ad Asclepium, sicut patet in libro de divinitate, 
qui satis habetur, cujus Asclepii avus fuit Aesculapius primus 
medicinae auctor apud infideles. Sed tamen Isidorus dicit in 
tertio libro etymologiarum, quod ApoUo fuit pater Aesculapii, 
qui primus inter philosophos infideles dicitur docuisse artem 
medicinae. Nam et patri ascribitur medicina quantum ad 
prima documenta ; sed filio magis, qui hanc artem applicavit 
et certiori modo docuit. Nam Apollo per carmina et hujus- 
modi remedia processit, Aesculapius per veritatem experientiae, 
Isidorus dicit, et creditur esse ApoIIo magnus, qui a poetis 
fingitur esse inter Deos et dare responsa in templo ApoIIinis 
in Delphis, unde vocatur Apollo Delphicus. Et tamen ante 
istos fuit inaestimabilis gloria medicinae, secundum quod 
Aristoteles tangit in libro de regimine vitae^, quam Adae et 

^ De Civiiate Deiy lib. xviii. cap. 8. 

' Another title for the Secreium Secreiorum, 



pius. 



PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 49 

Enoch magis ascribit quam sequentibus philosophis. Et cum 
medicina magis sit necessaria homini quam multae aliae 
scientiae, non est dubium quin filii Adae ct Noe illam 
invenerunt, quibus sapientiae plenitudo data fuit, et quibus 
concessum est tam diu vivere propter studium sapientiae 
perficiendum. 

Capitulum X. 

Post hoc, tempore Othonielis Judicis Israel, regnavit Cadmus. 
Cadmus Thebaeus, qui primus dedit literas Graecis^ ut in 
chronicis Cluniacensibus edocetur. Et Beda in libro tem- 
porum juniori et caeteri concordant, quod sub Aoth judice 
Amphion musicus floruit, qui Aoth fuit proximus post 
Othonielem. Et sub Barach fuit alius Apollo philosophus 
secundum Chronicam Cluniacensem, auctor medicinae, tem- 
poraneus Herculi secundo, cujus facta celebrantur ; sicut dicit 
Augustinus decimo octavo libro de Civitate Dei *. Qui Her- 
cules in tempore Abimelech judicis Trojam devastavit, et pilas Herculcs. 
suas in India statuit, et in Gadibus columnas erexit, et dolorem 
morbi non ferens seipsum tempore Jepthae judicis cremavit, 
ut per Augustinum decimo octavo libro, et dicta chronica con- 
firmatur. De hoc Hercule secundo propter hoc narravi, quia 
alius fuit Hercules prope tempus Mercurii majoris, qui parum 
post eum fuit, ut narrat Augustinus, et post eum fuit tertius, 
qui certamen Olympiacum constituit, quod intermissum filius 
ejus instauravit post excidium Trojae anno 408, ut Solinus 
scribit. Unde multi decepti fuerunt, unum esse Herculem 
aestimantes, qui omnia fecerit, quae de pluribus scripta sunt. 

Similiter erratum est de hoc philosopho Apolline. Nam Apoila 
omnes, ut dicit Augustinus, aestimant ipsum fuisse illum, qui * 
pro Deo in Delos insula colebatur, tanquam unus et idem 
esset ; cujus contrarium ostenditur multis testimoniis. Nam 
ille Apollo, qui in templis dabat testimonia, invenitur saltem 
respondisse quando primo facta est civitas Athenarum, ut 
Athena^ quae est Minerva, pro Dea coleretur ; et hic philo- 
sophus non potest esse^ qui pro Deo Delphico colebatur. Sed 

' omitted in J. 
VOL. I. E 



50 OPERIS MAJORIS PARS SECUNDA. 

iste, de quo dicit Augustinus, fuit filius Latonae, cujus soror 
Diana. Et Isidorus tertio libro idem dicit. Similiter non 
videtur esse ille, de quo Hieronymus scribit in epistola ad 
Paulinum, quae bibliis praeponitur Latinorum ; nam ille 
Hiarcum invenit in aureo throno sedentem et docentem, qui 
Hiarcus dicitur esse Abrachis ^ astronomus, qui post mortem 
Alexandri magni fuit, sicut docet Ptolemaeus in Almagesti. 
Et ideo secundum hoc tres fuerunt Apollines, sicut Hercules. 
Deinde sub Gideone fuerunt Orpheus et Linus, secundum 
Orpheus. quod Beda refert Et hi, scilicet Amphion, Orpheus, et 
Linus, suo tempore dicti sunt poetae theologi, secundum 
quod Augustinus dicit ^, eo quod Diis carmina faciebant ; 
secundum autem Solinum Nicostrates mater Evandri regis 
Romani dicta est a vaticinio Carmentis, quae in Capitolino 
monte Romae habitavit, et Latinis primo literas dedit Et 
haec, ut Beda refert, fuit tempore Jair judicis Israel ; secun- 
dum tamen chronicam Cluniacensem fuit tempore Judicis 
post Jair, transactis septemdecim annis. Sed de hoc non 
est cura quantum ad praesentem intentionem. 
Eryihraean Propter Sibyllas vero et maxime Erythraeam, quae omnes 
Sibyl. praedictos et praedictas philosophantes infideles longe super- 
gressa est, oportet etiam nos aliqua certificare. Nam 
Augustinus refert octavo decimo de Civitate Dei, quod 
multi auctores scripserunt eam fuisse tempore Trojani 
belli, et alii voluerunt eam fuisse tempore Romuli, et Achaz 
vel Ezechiae regis Judae. Et excidium Trojae fuit ante 
Romulum per quadringentos triginta annos. Nam Solinus 
probat Romam fuisse conditam Olympiade septima quadrin- 
gentesimo tricesimo tertio anno post bellum Trojanum, 
sicut docet evidenter per Herculem et Picum filium suum 
et per alios. Et secundum Augustinum, octavo decimo de 
Civitate Dei, vult quod Troja capta sit judicante Hebraeos 
Abdon. Deinde Hesiodus philosophus successit Homero 
ante Romam conditam, ut ait TuUius in quaestionibus Tus- 
culanis. Et postea Archilochus, regnante Romulo, sicut ibi 
describitur, et tempore Achaz vel Ezechiae regis Judae. Et 

* Abrachis or Abraxis was Ihe Arabian spelling of Hipparchus. 
' D« Civitait Dn, lib. xviii. cap. 14. 



PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 51 

similiter regnaverunt Numitor et ejus nepos Romulus, et tunc 
cessavit regnum et nomen Albanorum, et vocati sunt Romani 
reges. Et rex tunc erat in Judaea Achaz, vel sicut alii 
putant, Ezechias ; et sub eodem Romulo Thales Milesius 
fuisse perhibetur, qui fuit unus de septem sapientibus, et 
primus secundum Augustinum^ 



Capitulum XI. 

Nam post poetas theologos crevit sapientia, et auctores Scven wisc 
sapientiae vocati sunt Sophi, i.e. sapientes ; secundum tamen J^J^^. 
Bedam in libro temporum, et secundum Isidorum quinto 
Etymologiarum, Thales fuit sub Josia, qui rerum naturas 
scrutatus est, et fuit astrologus. Tempore quo populus 
Hebraeorum, ut Augustinus refert, ductus est in captivitatem, 
alius de septem sapientibus apparuit, scilicet, Pittacus nomine, 
et alii quinque fuerunt tempore captivitalis, quorum nomina 
sunt haec, Solon Atheniensis, Chilon Lacedaemonius, Peri- 
ander Corinthius, Cleobulus Lydius, Bias Pierius. De his 
Solon dedit leges Atheniensibus, ad quas transferendas decem 
viros populus Romanus misit, et vocantur leges duodecim tabu- Pytha- 
larum, sicut scribit Isidorus quinto libro. Aliud vero genus ^J^JYtoUan 
hominum sapientiae deditum post eos exortum est in lingua school. 
Graeca, quae tamen vocatur Italica. scilicet ex ea parte, quae 
Italia dicebatur, antiquitus Magna Graecia, et hi studuerunt in 
Italia licet Graeci, etiam in lingua Graeca. Et isti non 
voluerunt se vocari sapientes sed amatores sapientiae, quorum 
princeps fuit Pythagoras Samius a Samo insula ; a quo cum 
quaereretur, Quis esset, respondit, philosophus, i.e. amator 
sapienliae: sicut dicit Augustinus* octavo de Civitate Dei. 
Sed octavo dccimo libro dicit, quod Pythagoras apparuit eo 
tempore quo Judaeorum soluta est captivitas, et secundum 
TuUium in libro primo quaestionum Tusculanarum, Tarquinio 
Superbo regnante Romanis, qui fuit septimus a Romulo, et 
ultimus rex Romanorum. Postquam consules exorti sunt, 
venit in Italiam Pythagoras, et illam Magnam Graeciam tenuit 

' De Cwitafe Dei, lib. xviiL cap. 34. 
' Ibid. lib. viii. cap. a. Cf. lib. xviii. cap. 35. 
£ 2 



5a OPERIS MAJORIS PARS SECUNDA. 

cum honore, cum disciplina, cum auctoritate, et postea sic 
viguit Pythagoreorum nomen, ut nulli alii docti viderentur. 
Et Tarquinius, ut scribit Beda, tempore Cyri regis Persarum, 
qui laxavit captivitatem Judaeorum, incepit . regnare. Ac 
regnavit tempore Cambysis filii ejus, et duorum fratrum 
magorum, et Darii, in cujus anno secundo templum aedi- 
ficatum est. Et tunc clarus Pythagoras, ut dicit Beda, 
habebatur, et Zorobabel. Aggaeus, Zacharias, et Malachias 
prophetae claruerunt. Pythagoras quidem edoctus fuit a 
Pherecide Syro, ut dicit Tullius libro praedicto, qui Phere- 
cides primus animas hominum posuit immortales, cujus tem- 
pora non certificantur nisi per tempus Pythagorae discipuli 
sui ; quamvis et Isidorus libro primo dicat, quod Pherecides 
scripsit historias tempore Esdrae, qui potuit forte esse vcrsus 
finem vitae ipsius Pherecidis et in juventute Esdrae. Nam 
a tempore, quo dictus Pythagoras dicitur floruisse, fluxerunt 
triginta sex anni quibus regnavit Darius, et decem quibus 
Xerxes, et septem menses quibus Arthabas, et sex anni 
quibus Artaxerxes Longimanus, antequam Esdras ascendit 
de Babylonia in Jerusalem. Nam septimo anno r^ni ejus, 
primo die mensis primi, Esdras secundum Scripturas et 
chronicas profectus est. 

Capitulum XII. 

The Tonic Haec autem duo genera philosophantium, scilicet lonicum 

ing^ ^ ^t Italicum, ramificati sunt per multas sectas et varios succes- 

Socrates, sores usQue ad doctrinam Aristotehs, qui correxit et mutavit 

Aristotie. omnium praecedentium positiones, et philosophiam perncere 

conatus est. Successerunt vero Pythagoras, Archytas Taren- 

tinus, et Timaeus, inter alios maxime nominati. Sed prae- 

cipui philosophi, ut Socrates et Plato et Aristoteles, non 

descenderunt ex hac linea, immo vero lonici et veri Graeci 

fuerunt; quorum primus fuit Thales Milesius. Quomodo 

autem huic caeteri successerunt, ostendit Augustinus octavo ^ 

libro de civitate Dei. Nam post Thaletem fuit primus 

Anaximander ejus discipulus, cujus successor fuit Anaximenes, 

* Cap. a. 



PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 53 

et hi duo fuerunt tempore Judaicae captivitatis. Augustinus 
et alii similiter concordant in hoc. Anaxagoras vero et 
Diogenes Anaximenis auditores fuerunt, et eidem succes- 
serunt sub Dario Hydaspis, cujus anno secundo templum 
coepit aedificari. Anaxagorae, ut dicit Augustinus, successit 
Archelaus ejus discipulus, cujus auditor fuit Democritus 
secundum Isidorum octavo libro. Et Socrates, secundum 
Augustinum octavo libro, Archelai fuisse discipulus perhi- 
betur. Socrates autem secundum Bedam natus est sub 
Arthaba, qui Persis regnavit mensibus septem, cui in idem 
r^;num successit Artaxerxes Longimanus, in cujus anno 
septimo Esdras descendit de Babylone, et ideo simul fuerunt 
Esdras et Socrates. Sed prior natu fuit Esdras, sicut ex nunc 
dictis claret. Et ideo dicit Augustinus decimo octavo libro 
de Civitate Dei, quod post Esdram fuit Socrates, i.e. posterior 
natu. Nam quando floruit Esdras apud regem Persarum et 
Judaeos, tunc Socrates exortus est. Hic Socrates dicitur 
pater philosophorum magnorum, quoniam Platonis et Aris- 
totelis magister fuit, a quibus omnes sectae philosophantium 
descenderunt. Plato quidem, secundum Bedam in tractatu 
majori de temporibus, natus est sub Sogdiano, qui mensibus 
septem regnavit, cui successit Darius C(^nomine Nothus, 
quanquam sub eodem Dario Beda in eodem tractatu de 
temporibus scribat natum esse Platonem. Sed in illo tractatu 
tempus Sogdiani, quia modicum fuit, computat sub regno 
Darii. Nam continuat eum cum Artaxerxe Longimano. 
Nascente vero Platone, Hippocrates medicus, ut dicit Beda, 
habetur insignis, et hoc tempore Empedocles et Parmenides 
inventi sunt ; sed Plato Socratica primo addiscens, et ea quae 
Graeca fuerunt, Aegyptum petiit, ad Archytam Tarentinum, 
et Timaeum laboriosissime peragravit, ut dicit Hieronymus 
ad Paulinum. Et contra Rufinum scribit Hieronymus, quod 
Plato post Academiam et innumerabiles discipulos sentiens 
multum deesse suae doctrinae, venit ad Magnam Graeciam, 
ibique ab Archyta Tarentino eruditus, elegantiam et leporem 
cum hujusmodi miscuit discipulis. Et iste Plato omnibus 
philosophis antefertur secundum sanctos, quoniam ejus libri 
ad eorum manus devenerunt, et quia sententias de Deo 



54 OPERIS MAJORIS PARS SECUNDA. 

pulchras, et de moribus et de vita futura multa conscripsit quae 
sacrae Dei sapientiae multum concordant, ut in morali Philo- 
sophia explanabo ; et ab hoc aestimaverunt multi Catholici 
viri quod audiverat Jeremiam prophetam in Aegypto. Nam 
Aegyptum petiit propter sapientiam, et a barbaris sacerdo- 
tibus instructus est, ut scribit Tullius libro Academicorum 
quinto. Sed tamen Augustinus dicit quod non fuit tempore 
Jeremiae. Nam Jeremias ut dicit nono de Civitate Dei, 
primo prophetavit tempore quarti regis a Romulo qui vocatus 
est Ancus Martius^ et in tempore quinti regis scilicet 
Tarquinii Prisci. Sed Plato tunc non fuit ; immo post tempus 
Jeremiae fere per annos centum, ut dicit Augustinus octavo 
libro, natus est Plato. Sed ut alii aestimabant invenit LXX 
interpretes a quibus instrueretur, sicut Augustinus dicit octavo 
libro. Et TuIIius libro de Senectute dicit quod Plato mortuus 
est LXXXP anno vitae suae, id est in fine Artaxerxis qui 
Ochus dicebatur, ut scribit Beda. 

Capitulum XIII. 
Aristotlc. Ante 2 vero mortem Socratis natus est Aristoteles, quoniam 
Averrhoe». P^^ ^^^^ annos auditor ejus fuit, sicut in vita Aristotelis 
legitur. Et secundum Bedam natus est sub Artaxerxe, qui 
successit Dario Notho. Et in decimo septimo anno vitae 
suae fuit auditor Socratis, et ipsum per tres annos audivit, et 
post mortem Socratis factus est auditor Platonis secundum 
Bedam, et ipsum audivit, viginti annis, ut in vita sua legitur. 
Et post mortem Platonis vixit quadraginta tres annis, unde 
in universo non vixit nisi sexaginta sex annis, sicut ex 
dictis patet. Et hoc similiter patet in Ubro Censorini de 
die natali, quoniam ipse Censorinus refert contra passionem 
mortalem per tres annos eum magnitudine animi magis 

* The remaining part of this paragraph is omitted in Jebb*s ed. 

* What foUows, as far as the last sentence but one in cap. 15, is omitted by O. 
from this second part, and interpolated in Part III between Tertio and Quarto ; 
as also is ihe last paragraph of Part II. Further, the order in which these para- 
graphs are placed in Part III is not the same as in J. O. proceeds : * Hoc 
Domino Alexandro notum ; et multis aliis potest hoc idem adhuc etiam ostendi 
per proprietates duas Metaphystcae,' &c. 



PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 55 

quam medicinae virtute luctatum fuisse. Hic Aristoteles 
magister Alexandri magni efTectus duo millia hominum 
misit per mundi regiones, ut naturas rerum exquirerent, 
sicut Plinius narrat in Naturalibus octavo libro et mille 
libros composuit, ut in ejus vita legitur. Hic enim prae- 
cedentium philosophorum errores evacuavit, et augmen- 
tavit philosophiam aspirans ad ejus complementum quod 
habuerint antiqui patriarchae, quamvis non potuit singula 
perficere. Nam posteriores ipsum in aliquibus correxerunt, 
et multa ad ejus opera addiderunt, et adhuc addentur usque 
ad finem mundi ; quia nihil est perfectum in humanis inven- 
tionibus, ut in prioribus est expositum. Hunc natura firmavit, 
ut dicit Averroes in tertio de Anima, ut ultimam perfectionem 
hominis inveniret. Hic omnium philosophorum magnorum 
testimonio praefcrtur philosophis, et philosophiae ascriben- 
dum est id quod ipse aflSrmavit; unde nunc temporis auto- 
nomatice Philosophus nominatur, in auctoritate philosophiae, 
sicut Paulus in doctrina sapientiae sacrae apostoli nomine 
inteUigitur ^. Quievit autem et siluit philosophia Aristotelis, 
pro majori parte aut propter occultationem exemplarium 
et raritatem, aut propter difficultatem, aut propter invidiam, 
aut propter guerras Orientis \ usque post tempora Mahometi, 
quando Avicenna et Averroes et caeteri revocaverunt philo- 
sophiam Aristotelis in lucem plenam expositionis. Et licet 
alia Logicalia et quaedam alia translata fuerunt per Boetium 
de Graeco, tamen tempore Michael Scoti, qui annis Domini 
1230 transactis apparuit deferens librorum Aristotelis partes 
aliquas de Naturalibus et Metaphysicis ^ cum expositoribus 
authenticis, magnificata est philosophia Aristotelis apud 
Latinos. Sed respectu multitudinis et magnitudinis suae 
sapientiae in mille tractatibus comprehensae, valde^ modicum 
adhuc in linguam Latinam est translatum, et minus est in usu 
vulgi studentium. Avicenna quidem praecipuus imitator et 
expositor Aristotelis, ct complens philosophiam secundum 
quod ei fuerit possibile, tripiex volumen condidit philo- 
sophiae, ut ipse dicit in prologo libri Sufficientiae ; unum 

» Om. in Jebb. ' Om. in Jebb. 

' Jebb has MaUiematicis. * vel, Jebb. 



56 OPERIS MAJORIS PARS SECUNDA. 

vulgatum juxta communes sententias philosophorum Peri- 
pateticorum, qui sunt de secta Aristotelis; aliud vero se- 
cundum puram veritatem Philosophiae, quae non timet ictus 
lancearum contradicentium, ut ipse asserit ; tertium vero fuit 
cum termino vitae suae, in quo exposuit priora^, secretiora 
naturae et artis recolHgens. Sed de his voluminibus duo non 
sunt translata ; primum autem secundum aliquas • partes 
habcnt Latini, quod vocatur Assephae, i. e. liber sufficientiae. 
Post hunc venit Averroes, homo solidae sapientiae, corrigens 
dicta priorum et addens multa, quamvis corrigendus sit in 
aliquibus, et in multis complendus ^ 

Capitulum XIV. 

It is for Ex his sequitur necessario, quod nos Christiani debemus 

tieofo ^ns "^^ philosophia in divinis, et in philosophicis multa assumere 
to corry on theologica, ut appareat quod una sit sapientia in utraque 
t eirwor . j.giu^gjjg Quam necessitatem voluero certificare, non solum 
propter unitatem sapientiae, sed propter quod inferius tangam, 
oportet nos in philosophia revolvere sententias fidei et theo- 
logiae magnificas quas reperimus in libris philosophorum et 
in partibus philosophiae ; ut non sit mirum quod in philo- 
sophia tangam sacratissimas veritates, quoniam philosophis 
Deus concessit multas sapientiae suae veritates. Oportet 
igitur ut trahatur philosophiae potestas ad sacram veritatem 
quantumpossumus; nam valorphilosophiaealiternon lucescit^. 
Nam philosophia secundum se considerata nullius utilitatis 
est. Philosophi vero infideles damnati sunt, * et cum cogno- 
verunt Dominum, non sicut Dominum glorificaverunt et ideo 
stultificati sunt et evanuerunt a cogitationibus suis.' Et 
ideo philosophia non potest aliquid dignitatis habere, nisi 
quantum de ea requirit Dei sapientia. Totum enim residuum 

^ This is thc reading of Jul. 

' Jul. here adds a passage which firc has rendered illegible. The succeeding 
paragraph is headed, * Quarta Distinctio ; in qua ostenditur neccssitas utendi 
philosophia in divinis, non solum propter unitatem sapientiae perfectae sed quia 
in sequentibus partibus hujus persuasionis adductae sunt veritates divinae quae 
de pluribus philosophorum extrahuntur.' 

• * nam . . . lucescit,* supplied from Jul. 



PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 57 

est erroneum et inane, et propter hoc dicit Alpharabius in libro 
de scientiis, quod sicut puer indoctus se habet ad hominem 
sapientissimum in philosophia sic homo talis ad sapientiam 
Dei. Praeterea semper crescere potest in hac vita studium 
sapientiae, quia nihil est perfectum in humanis inventionibus. 
Quapropter antiquorum defectus deberemus nos posteriores 
supplere, quia introivimus in labores eorum, per quos, nisi 
simus asini, possumus ad meliora excitari ; quia miserrimum 
est semper uti inventis, et nunquam inveniendis, ut dicit 
Boetius, et probatum est efficaciter superius suo ioco. Item 
Christiani debent ad suam professionem quae sapientia Dei 
est caetera pertractare, et vias philosophorum infidelium com- 
plere ; non solum quia posteriores sumus, et debemus addere 
ad eorum opera, sed ut cogamus sapientiam philosophorum 
nostrae deservire. Nam hoc philosophi infideles faciunt ipsa 
veritate coacti in quantum eis datum est ; nam totam philo- 
sophiam reducunt ad divina ; ut ex libris Avicennae in Meta- 
physicae et Moralibus, et per Alpharabium et Senecam et 
Tullium, et per Aristotelem patet ; nam omnia reducunt ad 
Deum, sicut exercitus ad principem, inferentes de angelis et 
aliis multis, quoniam principales articuli fidei reperiuntur in eis. 

Nam ut in Moralibus exponetur, Deum esse docent, et They had 
quod sit unus in esse, infinitae potentiae et sapientiae et ^fmpses 
bonitatis, trinis in personis, Pater, et Filius et Spiritus Sanctus, ofChristian 
qui omnia creavit ex nihilo ; et de Domino Jesu Christo et de 
beata virgine multa tangunt. Similiter de Antichristo, atque 
de angelis et.custodia hominum per eos^ necnon de resurrec- 
tione mortuorum, et de judicio futuro, ct de vita futurae 
felicitatis quam Deus promisit obedientibus sibi, et de miseria 
futura, quam proponit inferre his qui mandata ejus non obser- 
vant. Scribuntque innumerabilia de morum honestate, de 
legum gloria, de legislatore qui debet accipere legem a Deo per 
revelationem, qui sit mediator Dei et hominum, et vicarius 
Dei in terra, et Dominus terreni mundi, de quo cum pro- 
batum fuerit quod recepit legem a Deo, ei credendum sit in 
omnibus, exclusa omni dubitatione et haesitatione, qui debet 
totum genus humanum ordinare in cultu Dei et l^ibus jus- 
* * per eos,' om. in O. 



58 OPERJS MAJORIS PARS SECUNDA. 

titiae et pacis, et in virtutum exercitio propter reverentiam 
Dei ac futuram felicitatem ; et quod idolonim cultura destrui 
debet. Haec et his similia ^ habuerunt philosophi. In libris 
enim eorum hujusmodi reperimus, sicut probatio certa doce- 
bit in sequentibus, et quilibet potest experiri qui vult libros 
philosophorum perlegere ; et negare non possumus quin 
scripta sunt ab eis, undecunque hujusmodi receperunt. Nec 
mirandum est quod philosophi talia scribant ; nam omnes 
phiiosophi fuerunt post patriarchas et prophetas, sicut prius 
de hoc facta est consideratio in suo loco; et legerunt libros 
prophetarum et patriarcharum qui sunt in sacro textu, et 
similiter alios libros, quos fecerunt tangentes Christi mys- 
teria ut in libro Enoch et in testamento patriarcharum 
in libro Esdrae, 3**, 4**, 5**, et in multis aliis libris de quorum 
aliquibus sit mentio in sacro textu ut de libris Nathan, 
Samuelis, et Abdon prophetarum. In hujusmodi enim libris 
tanguntur expresse articuli fidei, et longe expressius quam 
in Canone Scripturae. Nam praeter caeteros libros liber 
de testamentis patriarcharum ostendit omnia, quae de Christo 
impleta sunt. Quilibet enim patriarcha in morte praedicavit 
filiis suis et tribui suae, et praedixit eis ca quae de Christo 
tenenda sunt, sicut manifestum est ex libro suo. Et hi libri 
licet non sint in Canone, tamen sancti et sapientes Graeci 
et Latini usi sunt eis a principio Ecclesiae. Nam beatus 
Judas de hoc Enoch accepit auctoritatem, et Augustinus 
decimo de Civitate Dei, multum fundatur super illum librum, 
ut ostendatur quod primo fuit sapientia apud sanctos quam 
apud philosophos, et ait quod jam proptcr nimiam anti- 
quitatem ille liber non est in auctoritate, quam propter 
aliquid aliud. De libris autem aliis manifestum est quod 
in usu sanctorum et sapientum antiquorum sunt propter 
hoc quod planas veritates de Christo continere noscimus. 
Philosophi igitur curiosi et diligentes in studio sapientiae 
peragrarunt regiones diversas, ut sapientiam inquirerent, et 
libros sanctorum perlegerunt, et didicerunt ab Hebraeis 
multa. Nam Avicenna in radicibus moralis philosophiae 

' After ' similia* O has ' nunqiuun/ which is omitted in Jul., and which spoils 
the sense. 



PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 59 

recitat verba Esaiae de vita aeterna, dicens illam esse quam 
oculus non vidit, nec auris audivit, et recitat, Eleemosyna tollit 
peccatum, sicut propheta veritatisdicit, scilicet Tobias. Et 
Augustinus vult decimo octavo de Civitate Dei, quod Plato 
l^erat librum Geneseos, propter creationem mundi quam 
posuit similem ei quae ibi describitur. Et quod legis librum 
l^it, videlicet Exodi, propter nomen Dei quod ibi ponitur, 
scilicet, Ego sum qui sum. Nam hoc usus est Plato, et alibi 
non potuit invenire, ut dicit Aug^stinus. Et praeter sacros 
libros prophetales composuerunt libros philosophiae ; immo 
totam philosophiam his perfecerunt Et quod philosophi non 
habuerunt nisi ab eis, ostensum est in praecedentibus evi- 
denter, et quia una est sapientia, quae sufficit humano generi ; 
ideo sancti in libris philosophicis miscuerunt divina multa cum 
aliis, quantum potuit philosophia recipere. Et propterea 
propter istos libros philosophicos sanctorum multa percepe- 
runt philosophi de divinis veritatibus. 

Capitulum XV. 

Praeterea cum philosophi fuerunt dediti veritatibus et omni which in 
vitae bonitati, contemnentes divitias, delicias, et honores, oAhe^™' 
aspirantes ad futuram felicitatem quantum potuit humana Sibyls werc 

- ... . . rt- • 1 . TT. even more 

fragihtas, immo victores etlecti humanae naturae, sicut Hiero- expUcit 
nymus scribit de Diogene in libro contra Jovinianum, non 
est mirum, si Deus, qui in his minoribus illuminavit, daret eis 
alia lumina veritatum majorum. Et si non principaliter 
propter eos, tamen propter nos, ut eorum persuasionibus 
mundus disponeretur ad fidem. Et ad hoc facit quod Sibyllae 
multae inventae sunt, scilicet decem ; sicut omnes sancti 
concordant, et Augustinus decimo octavo de Civitate Dei *, et 
Isidorus libro Etymologicorum septimo. Necnon historiae 
et philosophiae et poetae concordant universaliter in his 
Sibyllis. Sed certum est eas recitasse divina, et ea quae de 
Christo habentur et de judicio futuro, et hujusmodi. Ergo 
multo magis probabile est quod philosophi sapientissimi et 
optimi a Deo receperunt hujusmodi veritates. Quod vero 

' Dt CiviiaU Dei, lib. zviii. cap. 23. 



6o OPERIS MAJORIS PARS SECUNDA. 

Sibyllae locutae sunt praeclare veritates divinas, manifestum 
est per sanctos et alios, et sufficit recitare quod Augustinus 
dicit decimo octavo de Civitate Dei ^. * Dixerunt igitur istae 
mulieres hujusmodi sermones ; dabunt Deo alapas manibus 
incestis, imputato ore exspuent venenatos sputus ; dabit 
vero ad verbera simpliciter suum dorsum, colaphos accipiens 
tacebit^ et corona spinea coronabitur. Ad cibum autem fel, 
et ad potum acetum dederunt. Insipiens gens, Dominum 
tuum non intellexisti ludentem mortalium mentibus, sed 
spinis coronasti, et horridum fel miscuisti. Templi vero 
velum scinditur, et medio die nox erit tenebrosa tribus 
horis, et morte morietur tribus diebus^ somno suscepto/ 
Et iterum metrice dixit Sibylla, 

*Judicii signum, tellus sudore madescet, 
Ex coelo rex adveniet per secla futurus, 
Scilicet in carne praesens ut judicet orbem. 
Unde DeuHi cernent incredulus atque fidelis, 
Celsum cum sanctis ejus jam termino in ipso. 
Sic animae cum came aderunt, quas judicet ipse. 
Exuret terras ignis pontumque polumque; 
Sanctorum sed enim cunctae lux libera carni 
Tradetur, sontes aetemum flamma cremabit. 
Actus occultos retegens tunc quisque loquetur 
Secreta, atque Deus reserabit pectora luci. 
Eripitur solis jubar et choms interit astris: 
Solvetur coelum, lunaris splendor abibit. 
Dejiciet colles, valles extollet ab imo. 
Sic pariter fontes torrentur, fluminaque igni, 
Tartareumque Chaos monstrabit terra dehiscens, 
Excidet e coelis ignisque et sulphuris amnis ^.' 

Si igitur mulierculae fragiles hujusmodi dixerunt, longe 
magis credendum philosophos sapientissimos hujusmodi gus- 
tasse veritates. Et Augustinus vult decimo octavo de Civi- 
tate Dei, alios percepisse Dei veritatem, quam illi qui de linea 
Abraham usque ad Christum et deinceps descendemnt Nam 

* Quoted by St. Augustine from Lactantius. 

■ This passage from the Sibylline poem is given most incorrectly in the MSS. 
I have corrected it from De Cwitatt Det\ lib. xviii. cap. 33. 



PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 6i 

Job scivit resurrectionem et Dei veritates. Et in chronicis 
Eusebii legitur, quod Irene et Constantiho imperantibus fuit 
cadaver effossum, in quo inveniebatur scriptura haec, * Credo 
in Christum ; sub Irene et Constantino iterum videbit me 
Sol/ Et nunc tempore Domini Alexandri Papae quarti 
Saracenus in Borea mundum contemnens, vacans in lege sua 
Deo et virtuti et contemplationi alterius vitae, recepit visita- 
tionem angelicam et consilium ut converteretur ad fidem 
Christi, et baptizatus est. Hoc Domino Alexandro notum 
est et multis aliis, et adhuc recolunt quamplures. 

Capitulum XVI. 

Potest hoc idem adhuc etiam ostendi per proprietates duas Philoiiophy 
metaphysicae. Nam haec scientia est de illis, quae omnibus J^s*^o^im^ 
rebus et scientiis conveniunt, et ideo ostendit numerum perfection 
scientiarum, et quod oportet esse aliam scientiam ultra philoso- hlghcr** 
phiam, cujus proprietates tangit in universali ; licet in *™^s of 
particulari non posset eam assignare. Scit enim philosophia 
suas imperfectiones, et quod deficit a plena cognitione eorum 
quae maxime sunt cognoscenda. sicut Aristoteles docet in 
Metaphysica ; et Avicenna similiter, ut tactum est superius. 
Et propter hoc devenit philosophia ad inveniendam scientiam 
altiorem, quam dicit esse scientiam divinorum, quam Theolo- 
giam perfectam vocant philosophi, et ideo philosophia elevat 
se ad scientiam divinorum. Item solliciti fuerunt philosophi 
super omnia inquirere scctam in qua esset salus hominis, et 
dant modos probandi hic praeclaros, sicut ex moralibus 
manifestum est. Et invenerunt certitudinaliter, quod aliqua 
debet esse secta fidelis et sufficiens mundo, cujus proprietates 
assignant, quae non possunt reperiri nisi in secta Christi, ut 
probatur suis locis, et ostenditur quod de bonitate Dei est de 
necessitate humana quod sciatur haec secta fidelis. Sed non 
potest hoc probari infiddibus per legem Christi, nec per 
auctores sacros, quia ex lege disputationis possunt negari 
omnia quae in l^e Christi sunt, sicut Christiani negant ea 
quae in aliis legibus continentur. Et etiam quia Christum 
negant, non est mirum, si auctores Christianorum negent. 



62 OPERIS MAJORIS PARS SECUNDA. 

Persuasio autem fidei necessaria est ; sed non potest hoc esse 
nisi duobus modis, aiit per miracula quae sunt supra fideles 
et infideles, de quibus nulius potest praesumere ; aut per viam 
communem fidelibus et infidelibus ^ ; sed hoc non est nisi per 
philosophiam. Ergo philosophia habet dare probationes fidei 
Christianae. Articuli vero hujus fidei sunt principia propria 
theologiae ; ergo philosophia habet descendere ad probationes 
principiorum theologiae, licet minus profunde quam ad 
principia aliarum scientiarum. Et hoc modo supponatur ex 
hac ratione, donec veniatur ad probationem sectarum. Nam 
ibi ostendetur quod moralis philosophia efficacius theologia^ 
deservit in hac parte, et ideo licet secundum veritatem hujus- 
modi sunt theologica, nihilominus tamen sunt philosophica, sed 
propter theologiam. 

Capitulum XVI I. 

Mond Praeterea tota philosophia speculativa ordinatur in finem 

P Ui^TOn^ suum, qui est philosophia moralis. Et quia finis imponit 
nccting nccessitatem eis, quae sunt ad finem ut Aristoteles dicit 
secundo Physicorum, ideo philosophia speculativa semper 
aspirat ad finem suum, et erigit se ad eum, et quaerit vias 
utiles in ipsum, et propter hoc potest philosophia speculativa 
praeparare principia moralis philosophiae. Sic igitur se 
habent duae partes sapientiae apud infideles philosophos : sed 
apud Christianos philosophantes scientia moralis proprie et 
perfecte est theologia, quae super majorem philosophiam 
infidelium addit fidem Christi, et veritates quae sunt proprie 
divinae ^. Et hic finis habet suam speculationem praecedentem, 
sicut moralis philosophia infidelium habet suam ; quae igitur 
est proportio finis ad fincm, est proportio speculationis ad 
speculationem : sed finis ut lex Christiana supra legem philoso- 
phorum addit articulos fidei expressos, per quos complet l^em 
moralis philosophiae ^, ut fiat una lex completa. Nam lex 
Christi leges et mores philosophiae sumit et assumit, ut certum 
est per sanctos, ct in usu theologiae et ecclesiae. Ergo 

^ Thus in Jul. Jebb*s reading here is confused and inaccante. 

* Sic JuL Jebb*s reading, * in homlne/ is unintelligible. 
' This passage has been corrected firom Jul. 

* This is the reading of Jul. 



PHILOSOPHIAE CUM THEOLOGIA AFFINITAS. 63 

speculatio Christiandrum praecedens legem suam debet super 
speculationem alterius legis addere ea quae valent ad iegem 
Christi docendam et probandam, ut surgat una speculatio 
completa, cujus initium erit speculativa philosophorum in- 
fidelium, et complementum ejus erit superinductum theologiae, 
et secundum proprietatem legis Christianae. Et ideo philo- 
sophia apud Christianos debet sapere multum de divinis, pius 
quam apud philosophos infideles, et propter hoc debent 
philosophi considerare philosophiam, ac si modo esset de 
novo inventa, ut eam facerent aptam fini suo. £t ideo debent 
multa addi in philosophia Christianorum ; quae philosophi 
infideles scire non potuerant. Et hujusmodi sunt rationes 
exsurgentes in nobis ex fide et auctoribus legis et sanctorum 
qui sapiunt philosophiam ; et possunt esse communia philo- 
sophiae completae et theologiae. Et haec cognoscuntur per 
hoc quod debent esse communia fidelibus et infideUbus, ut 
sint ita nota cum proferuntur et probantur, quod negari non 
possunt a sapientibus et instructis in philosophia infidelium. 
Nam philosophi infideles multa ignorant in praesenti^ de 
divinis quae proponerentur eis, ut probarentur per principia 
philosophia completae, hoc est, per vivacitates rationis quae 
sumunt originem a philosophia infidelium ; licet complementum 
a fide Christi reciperent sine contradictione, et gauderent de 
proposita sibi veritate, quia avidi sunt sapientiae et magis 
studiosi quam Christiani. Non tamen dico, quod aliquid de 
spiritualibus articulis fidei Christianae reciperetur in probatione, 
sed multae veritates sunt communes rationales, quas omnis 
sapiens de facili reciperet ab alio, quamvis secundum se 
ignoraret. 

Non igitur mirentur philosophantes, si habeant elevare 
philosophiam ad divina et ad theologiae veritates et sanctorum 
auctoritates, et uti eis abundanter cum fuerit opportunum^, 
et probare eas cum necesse est, et per illas alias probare; 
quoniam proculdubio philosophia et theologia communicant 
in multis. Et sancti non solum loquuntur theologice, sed 
philosophice, et philosophica multipliciter introducunt. Et 
ideo Christiani, philosophiam volentes complere, debent in 

^ Sic O. ; J. has particulari. ' Sic JuL ; O. has optimum. 



64 OPERIS MAJORIS PARS SECUNDA. 

suis tractatibus non solum dicta philosophorum de divinis 
veritatibus colligere, sed longe ulterius progredi, usquequo 
potestas phiiosophiae totius compleatur. . Et propter hoc 
complens philosophiam per hujusmodi veritates non debet 
dici theologicus nec transcendere metas philosophiae ; quoniam 
ista quae sunt communia phiiosophiae et theologiae potest 
secure tractare et ea quae communiter habent recipi a fidelibus 
et infidelibus. Et talia multa sunt praeter dicta philosophorum 
iniidelium, quae tanquam propria infra limites philosophiae 
debet recte philosophans coUigere, ubicunque ea invenit, et 
tanquam sua habet congregare, sive in libris sanctorum, sive 
philosophorum, sive in sacra scriptura, sive in historiis, sive 
alibi. Nullus enim auctor est quin praeter principalem inten- 
tionem aliqua incidenter recitet quae sunt alibi magis propria ; 
et hujus causa est annexio scientiarum, quia quaelibet ab alia 
quodam modo dependet ; sed omnis, qui debito modo tractat, 
debet quae sunt propria ei assignare, et quae necessaria et 
suae competentia dignitati, et ideo ubicunque ea inveniat velut 
sua cognoscere, et tanquam propria habet rapere, et in locis 
propriis collocare. Propter quod philosophans Christianus 
potest multas auctoritates et rationes et sententias quam- 
plurimas de scriptis aliis, quoque de libris philosophorum 
infidelium adunare, dummodo sint propria philosophiae, vel 
communia ei et theologiae, et quae communiter habent fideles 
et infideles reperire. Et nisi hoc fiat, non perficietur, sed 
multum ei derogabitur. Et non solum debet hoc fieri propter 
complementum philosophiae, sed propter conscientiam Chris- 
tianam, quae habet omnem veritatem ducere ad divinam, ut 
ei subjiciatur et famuletur. Atque propter hoc, philosophia 
infidelium est penitus nociva, et nihil valet secundum se con- 
siderata, nam philosophia secundum se ducit ad caecitatem 
infernalem et ideo oportet quod secundum se sit tenebrae et 
caligo. 

Capitulum XVIII. 
Summary. jjis consideratis \ patet intentum principale ; et manifestum 
est quod omnes philosophi infideles et Poetae et Sibyllae et 

* From this point to the end of Part II is omitted here in O. and is transposed 
to Part III. Vide note on p. 54. 



PHILOSOPHJAE CUM THEOLOGIA AFFINITAS. 65 

quicunque sapientiae sunt dediti, inventi sunt post philosophos 
veros et fideles, qui fuerunt filii Seth et Noe cum filiis suis, 
quibus Deus dedit vivere sexcentos annos propter studium 
sapientiae complendum, ut dicit Josephus primo Antiqyitatum, 
asserens quod in minore tempore non potuerant complere philo- 
sophiam praecipue propter astronomiam in qua est major diffi- 
cultas, eo quod a caelestibus homines mortales multum distant ; 
sed Deus eis reyelavit omnia, et dedit eis vitae longitudinem, 
ut philosophiam per experientias complerent. Sed propter 
malitiam hominum qui abusi sunt viis sapientiae, ut Nimroth, 
et Zoroaster, et Atlas, et Prometheus, et Mercurius aut Tris- 
megistus, et Aesculapius, et Apollo, et alii qui colebantur 
sicut Dii propter sapientiam, Deus obscuravit cor multitudinis, 
et recidit paulatim usus phiiosophiae usquequo iterum Salomon 
eam revocavit et perfecit omnino, sicut Josephus docet octavo 
Antiquitatum. Et iterum propter peccata hominum evanuit 
studium sapientiae, donec Thales Milesius resumpsit eam, et 
ejus successores dilataverunt, usquequo Aristoteles consum- 
mavit, quantum fuit possibile juxta idem tempus. Sed isti 
ab Hebraeis didicerunt omnia, sicut Aristoteles dicit in libro 
secretorum, quoniam philosophi infideles, ut Nimroth et alii, 
fuerunt post Seth, Noe, Sem, et Abraham ; et post Salomonem, 
qui secundo perfecit eam, fuerunt reliqui philosophi infideles 
ut Thales et Pythagoras, Socrates et Plato, et Aristoteles. 
Ideo manifestum est, quod philosophiae perfectio fuit primo 
data sanctis, Patriarchis et Prophetis, quibus lex Dei similiter 
fuit ab uno et eodem Deo revelata ; quod non fuisset factum, 
nisi philosophia omnino esset sanctis Dei et I^i sacrae con- 
formis et utilis ac necessaria propter intellectum legis et 
excusationem et defensionem ; insuper ut fiat ejus persuasio, 
et probetur et communicetur et dilatetur ; nam omnibus his 
modis necessaria est, sicut discurrendo per partes singulas 
philosophiae apparebit £t ideo philosophia non est nisi 
sapientiae divinae explicatio per doctrinam et opus, et propter 
hoc una est sapientia perfecta, quae sacris literis continetur. 



VOL. I. 



PARS TERTIA 

HUJUS PERSUASIONIS. 

De Utilitate Grammaticae^ 

Know- Declarato igltui;, quod una est sapientia perfecta, quae sacris 

implics literis continetur per jus canonicum et philosophiam, qua 

*n1f mundus habet regi, nec alia requiritur scientia pro utilitate 

longaaces generis humani, nunc volo descendere ad ea hujus sapientiae 

knowledge magnifica, quae maxime vaient exponi. Et sunt quinque, 

is recordcd. sine quibus nec divina nec humana sciri possunt, quorum certa 

cognitio reddit nos faciles ad omnia cognoscenda. Et primum 

est Grammatica in linguis alienis exposita, ex quibus emanavit 

sapientia Latinorum. Impossibile enim est, quod Latini 

perveniant ad ea quae necessaria sunt in divinis et humanis, 

nisi notitiam habeant aliarum linguarum, nec perficietur eis 

sapientia absolute, nec relate ad ecclesiam Dei et reliqua tria 

praenominata. Quod volo nunc declarare, et primo respectu 

scientiae absolutae. Nam totus textus sacer a Graeco et 

Hebraeo transfusus est, et philosophia ab his et Arabico 

deducta est ; sed impossibile estquod proprietas unius linguae 

servetur in alia. Nam et idiomata ejusdem linguae variantur 

apud diversos, sicut patet de lingua Gallicana, quae apud 

Gallicos et Picardos et Normannos et Burgundos multiplici 

variatur idiomate. Et quod proprie dicitur in idiomate 

Picardorum horrescit apud Burgundos, immo apud Gallicos 

viciniores: quanto igitur magis accidet hoc apud linguas 

diversas? Quapropter, quod bene factum est in una lingua, 

' I have kept Uiis tide, which is given in all Uie MSS. But it must always 
be remembered that it is not grammar in the ordinao* acceptadon of the wordy 
but knowledge of certain foreign languages, of which Bacon b urging the im- 
portance. 



LINGUARUM COGNITIO, 67 

noa est possibile ut transferatur in aliam secundum ejus 
proprietatem quam habuerit in priori. 

Unde Hieronymus, in epistola de optimo genere inter- 
pretandi, sic dicit, * Si ad verbum interpretor, absurdum 
resonat' Quod si cuiquam videatur linguae gratiam inter- 
pretatione non mutari, Homerum exprimat in Latinum ad 
verbum. Si quis autem eundem in sua lingua per se inter- 
pretetur, videbit ordinem ridiculosum, et poetam eloquentis- 
simum vix loquentem. Quicunque enim aliquam scientiam 
ut logicam vel aliam quamcunque bene sciat, eam, etsi 
nitatur in linguam convertere maternam, videbit non solum 
in sententiis sed in verbis deficere. Et ideo nullus Latinus 
sapientiam sacrae scripturae et philosophiae poterit ut oportet 
intelligere, nisi intelligat linguas a quibus sunt translatae. 

Et secundo considerandum est quod interpretes non Many 
habuerunt vocabula in Latino pro scientiis transferendis, quia ^o Latin*^^ 
non fuerunt primo compositae tn lingua Latina. Et propter equivaient. 
hoc posuerunt infinita de linguis alienis, quae sicut nec intelli- 
guntur ab eis qui linguas ignorant, sic nec recte proferuntur 
nec scribuntur ut decet; atque, quod vile est, propter 
ignorantiam linguae Latinae posuerunt Hispanicam, et alias 
linguas matemas, quasi infinities pro Latino. Nam pro mille 
millibus exemplis unum ponatur de libro vegetabilium 
Aristotelis, ubi dicit, * Belenum in Perside pernitiosissimum, 
sed transplantatum Jerusalem fit comestibile.' Hoc vocabulum 
non est scientiale laico Hispanicorum. Nam jusquiamus vei 
semen cassilaginis est nomen ejus in Latino. Quae sicut 
multa alia prius ab Hispanis scholaribus derisus cum non 
intelligebam quod legebam, ipsis vocabula linguae maternae 
scientibus, tandem didici ab eisdem. 

Tertio, oportet quod interpres cptime sciat scientiam quam A tran»- 
vult transferre, et duas linguas a quibus et in quas transferat. ^^^„1^ 
Solus Boethius primus interpres novit plenarie potestatem know (i) 
linguarum. Et solus dominus Robertus, dictus Grossum (J) tL^two 
Caput, novit scientias^. Alii quidem mendici translatores J*'™?^^^^ 

^ ^ heishand- 

* Of this bold reformer of ecdesiastical abuses, and champion of civil h'berties, ^* 
Bacon is never tired of speaking^. He held the see of Lincoln from 1235 till 
his death in 1353. < Quietis nescius, multis adversans, quam plurimisque ei 

F a 



68 OPEBIS MAJORIS PARS TERTIA. 

defecerunt multum tam in scientiis quam in linguis ; quod 
ostendit ipsorum translatio. Nam tanta est perversitas et 
horribilis difficultas, maxime in libris Aristotelis translatis ^, 

adversantibus/ is Matthew Paris* description of bim. Visiting Pope Innocent 
IV in 1250 to protest against the abuses of the Hospitallers and Templars, and 
finding that his opponents had deafened the papal ear with bribes, ^ O gold, gold/ 
he cried, * how great is thy power, especially in the Court of Rome 1 ' In the 
last year of his life, he wrote to the Pope, plainly telling him that his vow of 
cbedience to the Church forbade compliance with his extortionate demands for 
money. * Filialiter et obedienter non obedio, contradico et rebello.' The Pope 
could not contain himself for anger. * Who is this mad old man/ hc cried, * who 
dares to sit in judgement on our actions V But Cardinal Aegidius and others re- 
strained his wrath. *If we are to tell the truth,' they said, 'the things he writes 
are true. He is a Catholic man of most holy lifc, more religious and more 
excellent than we. He is held for a great philosopher, deeply leamed in Latin 
and Greek literature, zealous for justice, a teacher in theological schools, 
a preacher to the people, a lover of chastity, an uprooter of simony.' (Matthew 
Paris, ad ann. 1353.) 

It would seem probable that his scientific works were written before his 
elevation to the bishopric. Among them are, LibeUus de pkysids limis angulis 
tt figuris per quas omnes acHones naturaies compleHtur ; a treatise De natura 
locorum ; and a treatise De artihus liberalihus. These were printed in Venice, 
1514. Among the Harleian MSS. are two, as yet unedited ; 740», a treatise 
on the Calendar; and 4350, on the Celestial Sphere. Of Greek, according 
to Bacon, his knowledge was but slight ; but he introduced several Greek 
scholars into England, one of whom, Nicolas, transiated the apocryphal 
Testaments of the twelve patriarchs, brought from Athens by John of Bastng- 
stoke. (Ct Matthew Paris, ad ann. 1352). It seems probable that Bacon in 
the early part of his career profited much from Grosst6te*s teaching. The 
language of the Libellus de physicis lineisj as to the propagation of force, and 
as to the laws of reflection and refraction, bears a remarkable resemblance to 
that of Bacon. 

^ Cantor, in his History of Mathematics^ speaking of the school of translation 
set up at Toledo in the twelfth century under the direction of Raymuud, the 
archbishop of that city, by Dominic Gundisalvi and John of Seville, remarks : 
'Their labours were conducted in a circuitous fashion which had its conse- 
quences. The Arabic was first translated into Castilian, and from this the 
Ljitin version was made. Bearing in mind that the Arabic text was taken from 
the Greek by men whose powers of translation were not wholly beyond 
suspicion, we may imagine what sort of Aristotelian philosophy reached the 
mediaeval student after three repetitions of bungling.* Cantor, vol. i. p. 684. 
Jourdain, in his work Recherches critiques sur fdge et rorigine des traducHons 
iatines d*Aristote i^Nouvelle ^dition, 1843), has supplied specimens of these 
translations which enable us to form some judgement of their value ; since he 
distinguishes those made directly from the Greek text from those made from 
Arabic versions. The latter are not so inferior to the former as might faave 
been expected ; probably because the Arab scholars of the tcnth and eleventh 
centuries knew more Greek than the European scholars of the twelfth and 



LINGUARUM COGNITIO. 69 

quod nullus potest eos intelligere. Sed quilibet alii contra- 
dicit, et multiplex reperitur falsitas, ut patet ex collatione 
diversorum interpretum et textuum diversarum linguarum. 

Et similiter in textu sacro inveniuntur falsa, et male translata 
quamplurima. Nam Hieronymus probat translationem LXX 
interpretum et Theodotionis et Aquilae multas habuisse 
falsitates, quae fuerunt vulgatae per totam Ecclesiam. Et 
omnes stabant maxime pro translatione LXX, sicut pro vita, 
et reputabatur Hieronymus falsarius et corruptor scripturarum, 
donec paulatim claruit veritas Hebraica per solum Hiero- 
n^onum in Latinum conversa. Ne tamen nimia novitae 
deterreret Latinos, ideo, ut ipse scribit, aliquando coaptavit 
se LXX interpretibus et aliquando Theodotioni, aliquando 
Aquilae, et ideo multa dimisit, et propter hoc remanserunt 
plura falsa. Nam ut Augustinus probat de doctrina Christi 
libro secundo male translatum est quod habetur in libro Sapien- 
tiae, 'Spuria vitulamina non dabunt radices altas.' Nam debent 
esse spuriae plantationes, ut Augustinus probat per Graecum. 
Et tamen Hieronymus dimisit hoc, sicut alia, propter pacem 
Ecclesiae et doctorum. Atque scitur manifeste, quod Hiero- 
nymus humanum aliquid passus aliquando in translatione 
sua oberravit, sicut ipsemet pluries confitetur. Nam quod 
decimum nonum male transtulerat Isaiae, resumit in saginali 
quinto dicens, *in eo quo transtulimus incurvantem et lasci- 
vientcm nos autem verbum Hebraicum acman dum celeriter 
scripto vertimus, ambiguitate decepti refraenantem diximus.' 
Et aliud quod in eodem capitulo male transtulerat revolvit 
dicens, * Melius reor proprium errorem reprehendere, quam 
dum erubesco imperitiam confiteri, in errore persistere. In eo 
veroquotranstuli, ** et erit terra Juda Aegypto in festivitatem," in 
Hebraico legitur agga^ quod interpretari potest etiam festivitas, 
unde aggus in festivum vertitur, et timory quod significantius 
Aquila transtulit gerosin^ cum aliquis pavidus et timens 
circumfert oculos, et adveniens formidat initium; ergo, si 
voluerimus in bonam partem accipere quod recordatio Judaeae 
Aegypto sit gaudii recte festivitas dicitur; sin autem, ut 

thirteenth ; although sometimes the Arabic translation was made from an inter- 
mediate Syriac veraion. 



70 OPERIS MAJORIS PARS TERTIA. 

arbitror, in timore pro festivitate vertitur in formidinem vel 
pavorem.* 

Quarta causa est et ratio hujus rei, quod quamplurima 
Partsof adhuc desunt Latinis tam philosophica quam theologica. 
nmi o?ilhe "^^"^ ^^^^ ^"^^ Hbros Machabaeorum in Graeco, viz. tertium, 
Fathcrs ct quartum, et Scriptura facit mentionem de libris Samuel et 
translatecl. Nathan et Gad videntis et aliorum, quos non habemus. Atque 
cum tota certificatio historiae sacrae sit a Josepho in Antiqui- 
tatum libris, et omnes sancti expositionum suarum radices ac- 
cipiant a libris illis, necesse est Latinis ut habeant illum librum 
incorruptum ; sed probatum est quod codices Latini omnino 
sunt corrupti in omnibus locis, in quibus vis historiae consistit ; 
ita ut textus ille sibi contradicat ubique, quod non est vitium 
tanti auctoris; igitur ex translatione mala hoc accidit et 
corruptione ejus per Latinos. Nec estremedium nisi de novo 
transferantur vel ad singulas radices corrigantur. Similiter 
libri doctorum magnorum, ut beatorum Dionysii, Basilii, 
Johannis Damasceni, et aliorum multorum deficiunt ; quorum 
tamen aliquos dominus Robertus praefatus episcopus vertit in 
Latinum, et alii quosdam alios ante eum ; cujus opus est 
valde gratum theologis. Et si libri istorum translati essent, 
non solum augmentaretur sapientia Latinorum, sed haberet 
Ecclesia fortia adjutoria contra Graecorum haereses et 
schismata, quoniam per sanctorum eorum sententias, quibus 
non possunt contradicere, convincerentur. 

Similiter fere omnia secreta philosophiae adhuc jacent in 

linguis alienis. Nam solum quaedam communia et vilia ut in 

pluribus translata sunt ; et de hujusmodi etiam multa desunt. 

So too of Nam libri integri omittuntur in mathematicis et in naturalibus 

and of ^^ ^^ logicalibus et aliis, praeter magna secreta scientiarum, et 

Aristotle. artium, et naturae arcana quae nondum sunt translata ; ut est 

secunda philosophia Avicennae, quam vocant orientalem, quae 

traditur secundum puritatem philosophiae in se, nec timet 

ictus contradicentium lancearum ; et tertia quae fuit conter- 

mina* vitae suae, in qua experientias secretas congregavit, 

sicut ipse in prologo primae philosophiae suae annotavit £t 

similiter cum Aristotdes complevit octo partes naturalis 

' 5«r, JuL O. has conscicntia. 



LINGUARUM COGNITIO. 71 

philosophiae principales, quae multas sub se continet scientias, 
de prima parte non habemus omnia, de aliis vero quasi nihil. 
Et eodem modo de metaphysica, quae sunt novem, cum ipse 
compleverit eas, nihil habemus quod de metaphysica uUa 
dignitate vocari potest propter defectus multiplices et prae- 
grandes. De mathematicis vero, cum sint quinque scientiae 
magnae, non habemus nisi primam, et parum de secunda. 
Etiam de logica^ deficit liber melior inter omnesalios, et alius The 
post eum in bonitate secundus male translatus est, nec potest ^fof\is 
sciri, nec adhuc in usu vulgi est, quia nuper venit ad Latinos, Log»c, viz. 
et cum defectu translationis et squalore. Nec est mirum si dico and Rhe- 
istos libros logicae meliores ; nam oportet esse quatuor argu- ^oric.isstill 
menta veridica ; duo enim movent intellectum speculativum seu 
rationem, scilicet dialecticum per debilem habitutn et initialem, 
qui est opinio, ut disponamur ad scientiam, quae est habitus 
completus et finalis, in quo quiescet mens speculando veritatem. 
Et hic habitus non adquiritur per demonstrationem. Sed cum 
voluntas seu intellectus practicus sit nobilior quam specula- 
tivus, et virtus cum felicitate excellit in infinitum scientiam 
nudam, et nobis est niagis necessaria sine comparatione, necesse 
est ut habeamus argumenta ad exercitandum per intellectum 
practicum, praecipue cum magis simus infirmi in hac parte 
quam in speculatione. Libenter enim gustamus de ligno 
scientiae boni et mali ; sed difficiles sumus ad lignum vitae, ut 
virtutem dignitatem amplectamur propter futuram felicitatem. 
Quapropter oportet quod habeat intellectus practicus sua 
adjutoria ut excitetur per propria argumenta, sicut speculativus 
per sua, et ideo necesse fuit ut traderetur de his argumentis 
quibus moralis philosophia et theologia utuntur abundanter. 
Nam sicut speculativae scientiae gaudent argumentis specu- 
lativis opinionis et scientiae nudae, sic practicae scientiae, 
ut theologia, et moralis philosophia practica, considerant 
argumenta, quibus ad praxim, i.e. ad opus bonum excitemur, 
et flectamur ad amorem felicitatis aeternae. Et hic sunt 
duo modi flectendi nos ; unus est qui promovet animam ad 
credendum et consentiendum et commiserandum, et ad com- 

' The indusion of Rhetoric and Poetic in Logic is restated in Part iv. ch. a, 
and also in Op. Tertmm, cap. 75. 



72 OPERIS MAJORIS PARS TERTIA. 

placendum, et eorum actus, et ad contraria cum necessitate. 
Et hoc argumentum vocatur rhetoricum, et est respectu 
intellectus practici, sicut argumentum dialecticum ad intel- 
lectum speculativum. Et hic habitus qui flectit nos ad 
amorem boni operis habetur per argumentum poeticum ; quia 
poetae, ut Horatius et alii Graeci et Latini, vitia prosequuntur, 
et virtutes magnificant, ut aUiciantur homines ad honorem et 
odium peccati. Nam, ut ille dicit, 

*Aut prodesse volunt, aut delectare poetae. 
Omne tulit punctum qui miscuit utile dulci.' 
Non enim parum prodest civibus, qui delectat in moribus ; 
oportet enim non solum docere, sed delectare et promovere. 
Unde tam poeta quam orator debet haec tria facere, ut 
docendo reddat auditores dociles, per delectationem faciat 
attentos, et promovendo seu flectendo cogat in opus. Et 
haec argumenta in salutiferis rebus sunt fortissima, in puris 
speculativis impotentia, sicut demonstratio efficacissima est in 
speculationibus nudis, sed impotens est omnino in practicis, 
et in his quae pertinent ad saiutem, secundum quod Aris- 
toteles dicit, primo moralis philosophiae, quod perprimum est 
mathematicum uti argumento rhetorico, et rhetorem demon- 
strationem experiri, quoniam, ut dicit secundo, haec scientia 
non est contemplationis gratia, sed ut boni fiamus. Aris- 
toteles igitur fecit libros de his argumentis, et Alpharabius 
in libro de scientiis aflirmat duas partes logicae debere 
constitui de his duobus argumentis, quia sola logica deberet 
docere cujusmodi sunt argumenta, et qualiter componantur 
propter usum omnium aliarum scientiarum. Et tunc logica 
speculativis scientiis per argumenta, videlicet duo, quae sunt 
dialecticum et demonstrativum, moralibus autem ministrat 
practica argumenta. Et quia theologia et jus canonicum 
mores et leges et jura determinant, ideo haec duo argumenta 
sunt eis necessaria. Etiam quamvis Latini nondum habent 
scientiam horum argumentorum secundum artis logicae tra- 
ditionem, tamen necessaria sunt multis modis, Qualiter autem 
componantur haec argumenta, non est ad praesens dicendum. 
Sed in hoc opere, quod Vestra Beatitudo postulavit dicitur 
explicari. Nihil tamen de scientiis speculativis utilius est 



LINGUARUM COGNITIO, 73 

propter fidem probandam infidelibus ut flectantur ad creden- 
dum et amorem fidei Christianae. Et similiter ut artificialiter 
praedicemus omnibus quibus praedicatio necessaria est, et sic 
de aliis utilibus persuasionibus ad salutem. Magnum autem 
adjutorium habemus per Augustinum in tertio et quarto de 
doctrina Christi, et per libros Tullianos, et per libros Senecae 
et epistolas, quae possunt colligi in lingua Latina de his argu- 
mentis, quamvis ipsa textura Aristotelis nobis deficiat. 

Quinta ratio est ad hoc, quoniam ex sensu sunt compositae The fathers 
et expositae, et ideo cum scientiae fuerunt traditae Latinis ^^jf^^J^g 
a linguis alienis, omnes sancti et philosophi Latini, qui ex- of foreign 

.... , . origin. 

ponunt scientias, usi sunt caeteris copiose, et multiphcant nobis 
vocabula Graeca et Hebraea et Chaldaea et Arabica, praeter 
ea quae in textibus continentur. Et nos sumus filii et suc- 
cessores sanctorum et sapientum usque ad haec ultima 
tempora. Nam vidimus aliquos de antiquis qui multum labora- 
verunt, sicut fuit dominus Robertus praefatus translator, 
Episcopus Lincolniensis, et dominus Thomas venerabilis 
antistes sancti David nuper defunctus, et frater Adam de 
Marisco, et magister Hermannus translator^ et quidam alii 
sapientes. Sed quoniam eos non imitamur, ideo ultra illud 
quod credi potest deficimus a potestate scientiarum, quia 
expositiones authenticas non possumus intelligere, et per eas 
nec intellectum scientiarum possumus obtinere. Et pro 
infinitis pono duo exempla. Hieronymus dicit in prologo 
Daniel, quod Daniel et Esdras scribuntur libris Hebraicis, sed 
Chaldaeo sermone, et una pericope Jeremiae. Hanc autem 
pericopen Jeremiae omnes theologi dicunt esse Threnos 
Jeremiae : quia pericope idem est quod pars parva seu par- 
ticula ; sed omnes Hebraei sciunt quod scribimus Threni literis 
Hebraicis et Hebraeo sermone. Deinde possumus hanc 
pericopen sumere decimo capitulo Jeremiae, ubi dicitur sic, 
• Ergo dicetis eis, Dii qui coelum et terram non fecerunt 
pereant de terra, de his quae sub coelo sunt.' Nam hoc 
tantum in Jeremia habet sermonem Chaldaeum, sicut omnes 
Hebraei sciunt literati. Et certum est quod Hebraei et 
Chaldaei eandem habent lingruam, sed diversum idioma, sicut 

^ Omitted in O. 



74 OPERIS MAJORIS PARS TERTIA, 

Gallicus et Picardus. Idioma enim est proprietas linguae 
apud aliquam nationem determinatam, unde Hebraeus dicit 
Eloim pro Deo vel Diis ; Chaldaeus dicit Eloa^ pro coelo vel 
coelis. Pro noii^ Hebraeus dicit lo, Chaldaeus dicit la^ et sic 
in aliis. 
The Tamen quod haec pericope scribatur sermone hic Hebraeo 

alphabet. ^^ Chaldeo, ponetur alphabetum ^ Hebraeum, ut facilius valeat 
intelligi quaestio proposita, et primo scribuntur figurae 
Hebraicae; secundo in linea superiori ponuntur nomina; et 
supremo assignantur litterae quae literis Hebraicis corre- 
spondent; ut literarum Hebraicarum sciamus virtutes et 
potestatem sonorum, secundum quod quaedam sunt vocales 
et quaedam consonantes. 



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P 




S 




n 


n 

taf 

t 


m 

shin 

sh 


1 
rish 

r 


ch 

P 
koph 

k 


ch 

tsadik 

ts 



Sunt autem sex vocales, viz. aleph, ain, he, heth, iot, vau ; 
reliquae sunt consonantes : he et heth aspirantur, ut he in 
principio, heth non solum in primo sed in fine, et generatur 
in gutture, he in ore ; aleph similiter in ore ; ain in gutture ; 
sed considerandum quod soium iot habet unum sonum sicut 
i nostrum, et sit consonans et vocalis sicut apud nos j. Vau 
vero, ut dicit Hieronymus in Hebraicis quaestionibus, habet 
duplicem sonum, viz. v nostrum et o : reliqua vero quatuor 
habent sonum quinque vocalium nostrarum, viz. a, e, i, 6, et u ; 
sicut patet per Hieronymum in libro interpretationum. Et 

^ Neither this Hebrew alphabet nor the Greek alphabet which follows will 
be found in Jebb*s edition, which has moreover manyother omissions, supplied 
here from Jul This is the more strange as Jebb undoubtedly had thts MS. 
before him. and made use of it in the first part. He had the advantage of using 
it a year or two before it was so damaged by fire as to rendcr much of it 
illegible. 



LINGUARUM COGNITIO. 75 

hanc diversitatem sonorum signant per puncta et tractus. 
Nam si sub aleph trahatur linea sine puncto sic, ^, vel cum 
puncto, K sonatur a. Si vero duo puncta fiant jacentia sub 
aleph e transverso S, vel duo stantia ^^, vel tria in modum 
trianguli ?, vel quinque puncta hoc modo g, sonatur e. Si vero 
tria puncta iaceant sub aleph ex obliquo descendentia sic *J 
sonatur u. Si vero unus punctus ponatur sub litera K sonatur 
i. Si vero unus punctus fiat supra sonatur o, sic, K. Et ita 
est de ain, et he, et heth, quae habent hos quinque sonos per 
istorum signorum diversitatem. Et cum vaf sonatur v potest 
esse signum trium punctorum ut dictum est sic 1,, vel potest 
poni unus punctus sic \ 

Ideo oportet quod ad consonantes ponantur haec signa, ut 
sdatur sonus vocalis syilabicandus cum consonante : ut si volo 
designare ba, be, bi, bo, bu, scribam sic: ? ? ? ^ ?[. Et 
habent alia signa per quae designant sonos consonantium 
aliquando fortificari aliquando remitti. Unde quando tractus 
ponitur super literam tunc remittitur: quando punctus in 
ventre ponitur tunc fortificatur. Ut quando super Dalct 
ponitur tractus sic i tunc debilem sonum reddit ut nostri z, 
ut cum dico, adamas, Quando punctus in ventre ejus col- 
locatur, sic, "^, tunc fortiter sonat, ut cum dico, dabo, . . . 

Manifestus ergo et vilis est error omnium in hac parte 
propter ignorantiam harum linguarum. 

Aliud exemplum accipiam de Graeco et multa exempla The Grcck 
Graeca addentur in sequentibus. Sed volo hic ponere alpha- *^P^*>^^ 
betum Graecum cum diphthongis quibus scribunt; multo 
enim evidentius per hoc patebit quae dicenda sunt. 

a b g d e z i th 1 

alpha vita gemma delta e pente zita ita thita iota 

o/3y b f C u i 

k 1 mnx o prst 

kappa labda mi ni xi o microo pi ro sima taf 

K A M^f o v p <r T 

y ph ch ps 
ypsilo phi chi psi o mega 
« 4» X V^ » 



76 OPERIS MAJORIS PARS TERTIA. 

Sunt autem septem vocales quantum ad figuras diversas, 
quum habent triplex i et duplex o ; sed quatuor tantum 
habent quantum ad sonum principalem, videlicet, a, e, i, o. 
Diphthongus apud Graecos est conjunctio duarum vocalium. 
Sonus unius vocalis habetur ut vocalis cum consonante. Et 
finales Hterae in diphthongis sunt iota et ipsilo. Potest 
igitur ipsilo consequi alpha sic, av, et tunc sonat quantum 
a cum V consonante, quia sonus aliquantulum similis est sono 
ipsius a cum f, et ideo vulgariter exemplificamus quod sonat 
af. Et potest consequi e, sic cv, et tunc sonat quantum 
e vocalis cum v consonante, quasi ef, ut dictum de alpha et 
ipsilo. Vel potest consequi iota, sic ti», et sonat quasi if, ut 
dictum de aliis. Vel ipsilo potest consequi o micron, sic ov, 
et tunc sonat u vocalem. Et sic solum habent Graeci sonum 
hujus vocalis u. Quum autem iota consequitur alpha sic, ai, 
tunc sonat e, quasi e. Quum e, sic ct, tunc sonat i per iota : 
si o, sic 01, tunc sonat y per ypsilo. Et hi octo diphthongi 
vocantur proprii. Et alii tres dicuntur improprii ; et fiunt 
per subscriptionem hujus literae iota ad alpha, ita, et o mega, 
sic, a, 77, ^. Aliquando ponitur iota in linea, sicut in aliis 
diphthongis sic at, T^t, a>i. Sed remanet sonus literae princi- 
palis, sciiicet ejus cui subscribitur iota. Nam cum subscri- 
bitur a, quae est alpha, sonat a : quum vero 77, quae est ita, 
sonat ita : si vero a>, quae est o mega, sonat solum o mega. Et 
his tribus diphthongis utuntur Graeci semper in dativo casu 
primae declinationis. 

... Et ^ licet exemplificare in praesenti loco de Jacob qui 
cum obviaret Esau fratri suo veniens de Mesopotamia et 
distaret dicit, Vidi faciem tuam quasi faciem Dei vidissem. 
Quaerit Augustinus, qualiter poterat homo sanctus hominem 
reprobatum comparare Deo ? et solvit quod multipliciter Deus 
in scriptura accipitur pro vero Deo, aliquando aliter. Et hoc 
multis modis : sed ut LXX interpretes designaverunt quod 
non loquebatur de vero Deo ideo apposuerunt articulum 
Graecum ad nomen dei. Nam hoc est de proprietate articuli 
ut veritatem rei designet. Sed hoc non apparet in Latino, 

' There is evidently a hiatus here. The subject considered is now the use of 
the article in Greek. 



LINGUARUM COGNITIO. 77 

quia Latini non habent articulum. Nam satis innotescit in 
Gallico. Unde cum dicitur Parisius Li reis venty iste arti- 
culus li designat proprium et verum regem talis loci, quasi 
regis Franciae. Et non sufficeret hoc ut denotaret adventum 
regis Angliae. NuUus enim diceret de rege Angh'ae veniente 
Parisius, Li reis vent, sed adjungeret aliud dicens, Li reis de 
Engletere vent. Et ideo articulus solus sufficit ad veritatem 
et proprietatem rei de qua est sermo designandam. Propter 
quod Augustinus dicit quod Graecum hoc sit irpoVdoiror ^«oC, 
quod in Graeco sonat prosopon theu ; cum articulo enim non 
sic, prosopon tu theu, Trpoaraynov tov $€ov, Prosopon hic signi- 
ficat vultum vel faciem. Theu est genitivus casus hujus 
nominis theos quod est Deus, et tu est articulus genitivi. 
Magna ergo necessitas est ut Latini sciant linguas propter 
dicta sanctorum et caeterorum sapientum. 

Sexta ratio est propter errorum falsitatum infinitarum The tcxt 
correctionem in textu tam theologiae quam philosophiae, non Bibi^^has 
solum in litera, sed in sensu. Quod autem correctio sit become 
necessaria, probo per corruptionis magnitudinem. Et quo- ^^pt^ ^ 
niam violentius et periculosius erratur in textu Dei quam 
textu philosophiae, ideo convertam h*nguarum potestatem 
ad corruptionem textus sacri, ut pateat necessitas earum, 
propter ^ corruptionem infinitam exemplaris vulgati quod est 
Parisiense. Et Deus novit quod nihil tam valida indigens 
correptione potest Apostolicae Sedi praesentari sicut haec 
comiptio infinita. Nam litera ubique in exemplari vulgato 
falsa est, et si litera sit falsa vel dubia, tunc sensus literalis 
et spirituahs falsitatem et dubitationem ineffabilem continebit, 
quod volo nunc ostendere sine contradictione possibili. Nam 
Augrustinus contra Faustum dicit, 'Si discordia in Latinis 
codicibus est, recurrendum est ad antiquos et plures. Nam 
antiqui praeponendi sunt novis, et plures paucioribus prae- 

^ From here to the end of thc following sentence, supplied from Jul. The 
comiption of the Biblical text is fuUy discussed in the Ofius Minus, under the 
head of the fifth sin of Theology (Brewer, pp. 330--349). See a]so the vaJuable 
Memoir of Abb^ Martin, La Vulgatt LaHfu au xtii' stkU d^apris Roger Bacon, 
Paris: Maisonneuve, 1888. The exemplar ParisUnst appears to have been 
a text very carelessly compiled about 1330, and probably very carelessly copied, 
to meet the demands of the multitude of students who were flocking to Paris. 



78 OPERIS MAJORIS PARS TERTIA. 

feruntur/ Sed omnes antiquae Bibliae quae jacent in mona- 
steriis, quae non sunt adhuc glossatae nec tactae, habent 
veritatem translationis, quam sacrosancta a principio recepit 
Romana Ecclesia, et jussit per omnes Ecclesias divulgari. 
^pwrially ged hae in infinitum contradicunt exemplari Parisiensi: 
text. igitur hoc exemplar magna indiget correctione per antiqua. 

Caeterum Augustinus ibidem dicit^ * Quod si dubitatio adhuc 
remaneat in antiquis bibliis, recurrendum est ad linguas, scilicet 
Hebraicam et Graecam * ; et hoc dicit secundo de doctrina 
Christiana, et ostendit in exemplis. Et Hieronymus hoc 
dicit ad Frecellam sororem et super Zachariam, et omnes 
sancti concordant ; sed antiquis bibliis concordant linguae 
Graecorum et Hebraeorum contra exemplar Parisiense ; igitur 
oportet quod corrigatur. Caeterum Hieronymus dicit ad 
Damascenum in hoc casu, ' Ubi est diversitas, non cst veritas 
nota/ Sed illi qui nituntur cum omni veritate quantum pos- 
sint corrigere textum sunt duo ordines Praedicatorum et 
Minorum. Jam de correctione formaverunt varias scripturas, 
et plus quam una biblia contineat; contendunt ad invicem, 
et contradicunt infinities, et non solum ordines ad invicem, 
sed utriusque ordinis fratres sibi invicem contrariantes plus 
quam ordines totales; nam omnis dominus alii contradicit, 
et in eadem correctores sibi invicem succedentes mutuas 
eradunt positiones cum infinito scandalo et confusione. Unde 
cum ad viginti annos praedicatores redegerunt correctionem 
in scripturis, jam venerunt alii, et novam ordinaverunt correc- 
tionem, quae continet plus medietate unius bibliae ; quantum 
vix ponatur in tanta scriptura quantum Novum continet Testa- 
mentum. Et quia vident se errasse in antiqua correctione, 
jam fecerunt statuta quod nullus ei adhaereat ; et tamen 
secunda correctio propter horribilem sui quantitatem simul 
cum veritatibus multis habet sine comparatione plures falsi- 
tates quam prima correctio. 
J/™*^*' Quod autem dixi in universali, potest patere in exemplis ; 

nam infinities accidit corruptio additione, subtractione, con- 
junctione, divisione orationis, dictionis, syllabae, literae, diph- 
thongi, aspirationis notae: et non solum litera, sed sensus 
literalis et spiritualis mutantur; et non solum cadunt haec 



tlODS. 



LINGUARUM COGNITIO. 79 

vitia circa unam orationem, sed circa multas, immo penes 
folia quamplurima; et de singulis unum ponam exemplum 
vel duo. Nam multi prologi superflui ponuntur in textu, cum 
non sint prologi textus in quibus redditur ratio translationis 
librorum quibus praeponuntur, sed sunt epistolae familiaribus 
missae, ut epistola Hieronymi ad Paulinum, quae in capite 
bibliae reputatur prologus et vocatur a vulgo, quae tamen in 
libro epistolarum Jeronymi continetur ; vel respectu prologi in 
commentarios et in originalia non in textum, sicut idem quod 
praemittitur ante librum Ecclesiastis. Nam patet quod pro- 
logus est ibi originalis, et patet ex sententia. Et sic est de 
multis aliis, quae non sunt in bibliis antiquitatis. De una 
oratione superflua est exemplum Deuteronomii 27. * Male- 
dictus qui dormit cum uxore proximi sui, et dicet omnis 
populus Amen ; ' quoniam nec antiqui codices, nec Hebraeus, 
nec Graecus habent versum hunc. De superfluitate dictionis 
horribile est ac nefandum octavo Genesis, cum dicitur quod 
*Corvus ad arcam non est reversus/ et Hebraei et Hieronymus 
in originali habent affirmativam. Et accepta est negatio a 
paucis temporibus de alia translatione, scilicet LXX inter- 
pretum, cujus fabitatem Hieronymus ostendit locis inflnitis, 
et jam a tempore Isidori et antea evacuata est. Nam ipse 
dicit in libro de officiis quod generaliter omnes ecclesiae Latinae 
utuntur translatione Hieronymi, pro eo quod veracior sit in 
sententiis et clarior in verbis ; excepto quod propter nimium 
usum psallendi in ecclesia solius psalterii translatio scilicet 
LXX interpretum remansit. Sed antiquitus Romana Ecclesia 
jussit translationem hanc ubicunque haberi. Augustinus et 
alii et ipsemet Hieronymus tempore suo usi sunt sicut Ecclesia 
translatione antiqua. Et ideo Augustinum quum recitat textum 
hunc decimo sexto de Civitate Dei et exponit oportuit quod 
uteretur translatione quae fuit vulgata et recepta apud Latinos, 
nec potuit aliud facere. Omnis vero glossator qui infixit glossas 
super textum accepit auctoritatem Augustini de Civitate Dei 
et eam posuit infra textum, sed non mutavit eam nec intulit 
n^ationem . . . inter caeteros hoc fecit. Et sic vulgatus est 
error horribilis cum contradictorium pro contradictione pona- 
tur. Nam videtur in philosophia quod ejusdem libri est 



8o OPERIS MAJORIS PARS TERTIA. 

aliquando duplex et triplex translatio ; et una habet diversum 
vel aliquando contrarium alteri. Sed nullus est qui ausus est 
translationem unam miscere cum alia. 

Quod autem ecclesiastici habent in legendo negationem hoc 
est de corruptione exemplaris apud studentes ad ecclesiasticos 
derivatum, et de syllabae mutatione, et per consequens totius 
dictionis. Et exemplum mirabile est de Joseph, qui dicitur 
in exemplari vuigato venditus fuisse triginta argenteis propter 
exemplum Domini^ sed secundum antiquos codices et He- 
braeum, et Graecum, et Arabicum, et Hieronymum in origi- 
nali, et Josephum in antiquitatum libro, debent esse viginti 
non triginta. Et similiter in Psalterio ad syllabae mutationem 
mutatur tota dictio cum infinito errore, cum dicitur, ' Sitivit 
anima mea ad Deum fontem vivum.' Nam cum ecclesia in 
solo Psalterio utatur translatione LXX interpretum, Hierony- 
mus correxit hanc translationem bis, et posuit fortem ubi 
ponimus fontem per errorem propter similitudinem dictionis, 
et propter hoc quod in praecedenti versu fit mentio de fonte ; 
sed ut dixi Hieronymus correxit/^/^»i, et ita est in Hebraeis 
bibliis et in psalteriis antiquis monasticis. Nam hoc diligenter 
inspexi ; et omnino certum est quod non est hic error viiissimus 
propter similitudines praedictas. 

De literae mutatione est exemplum notabile primo Judicum, 
cum dicitur in monte Ares, quod interpretatur testaceo, ut 
penultima litera sit e non i, sed communiter habetur testacio 
per i, ut sit nominativus casus, et idem quod testificatio a teste ; 
sed si deberet esse ablativus, derivatur a testa. Nam in omni- 
bus antiquis bibliis est testaceo per e, et in Graeco, et in 
Hebraeo, ubi habetur hares, Hieronymus transtulit testam^ 
vel aliquid derivatum a testa ; nam hares in Hebraeo testam 
vel aliquid praedictorum significat in Latino. Unde Hiero- 
nymus in sexto libro super Isaiam exponens idem verbum 
decimo sexto capite, * His qui laetantur super muros cocti 
lateris,' dicit hares testam sive coctum laterem significat. Et 
in decimo octavo libro super idem vicesimo quarto Isaiae, 
*Erubescet luna,' dicit quod hares testam sive coctum vel 
ariditatem sonat. Quod vero tricesimo primo et tricesimo 
secundo Jeremiae confunduntur haec nomina Ananeel et 



LINGUARUM COGNITIO, 8i 

Anameel per errorem, ut in litera indifferenter ponitur m in 
penultima, est error magnus in mutatione unius literae. Nam 
Hieronymus dicit in originali, quod Ananeel per n scriptum est 
tuiTis, per m est filius patruelis Jeremiae, et sic invenitur in 
Hebraeo. De aspirationis nota exemplum primo ad Thessa- 
lonicenses, cum dicitur, ad cujus orey ut sit ablativus casus 
hujus nominis oSj oris^ et non genitivus hujus nominis hora^ 
horae ; scribitur enim in ablativo casu, et glossatur non a sancto, 
sed a magistro sententiarum, qui glossavit epistolas ; sed sicut 
defecit multiph'citer in expositione propter ignorantiam Graeci, 
ita fecit hic. Quum procul ^ dubio in Graeco, a quo sumptus 
est genitivus hujus nominis hora, invenitur horas, et aspiratur 
tam apud Graecum quam apud Latinum. Scilicet Os, orisy non 
aspiratur. Hoc enim verbum, hora^ est Graecum, licet Latino 
nomine declinatur, sicut Domina: sed Graecus declinat sic, 
hora, horas, hora, horam, hora. Unde nominativus et dativus, 
et vocativus, similes sunt : accusativus in am, genitivus in as ; 
ablativum non habent Graeci. Et hoc in Graeco est horas, 
sicut ego legi dihgenter et omnibus possim probare qui sciunt 
Graecum, et in Graeco invenitur aspiratio. Haec exempla 
volui assumere ut quae probant quod necesse est linguas sciri 
propter textus Latini corruptionem tam in theologia quam in 
philosophia. Quomodo vere de corruptione plene probo et 
in speciali per omnes corruptiones bibliae, in aliud tempus 
differtur propter rei magnitudinem quae potest Vestrae Sancti- 
tati praesentari, sed non nunc ut suflliciat, sed magis per alium 
in sequentibus explicabo. 

Septima ratio est, quia necesse est ut Latini sciant linguas Even when 
specialiter propter sensus falsitatem, etsi litera esset verissima. corrcS\ris 
Nam tam in theologia quam in philosophia necessariae sunt wrongly 

^x- ^- -x-. ^-xx intcrpreled. 

mterpretationes et praecipue m textu sacro, et m textu 
medicinac et scientiarum secretarum ; quae nimis occultantur 
propter ignorantiam interpretationum. Nam medici confusi 
sunt propter malas interpretationes, quas vocant synonyma ; 
non est autem eis possibile uti medicinis authenticis propter 
errorum istorum synonymorum ignorantiam ; et ideo accidit 

* The followiiig passage, down to the end of the paragraph, is omitted in 
O. and D., and has been supplied from Jul. 
VOL. I. G 



82 OPERIS MAJORIS PARS TERTIA. 

in manibus eorum infinitum periculum. Eodem modo est in 
textu sacro; nam summa difficultas, quae est apud ipsum 
sciendum est propter varietatem et obscuritatem infinitarum 
interpretationum, et in exemplo famiiiari pro infinitis aliis 
apparet. Vulgus enim hoc nomen Israel pro patriarcha inter- 
pretatur virum videntem Deum. Et praevaluit hoc in usu 
usque ad tempus Hieronymi, et etiam usque quo sua translatio 
et sua expositio jussae sunt per omnes ecclesias divulgari. 
Sed ipse dicit in originali quantae grandis auctoritatis sunt^ et 
eorum verbis nos opprimit qui Israel virum videntem Deum 
interpretati sunt. Nos tamen magis consentimus Domino vel 
Angelo qui illi hoc nomen imposuit quam auctoritati alicujus 
saecularis eloquentiae. Et ideo probat egregie quod affirmat. 
Nam illi qui sic interpretati sunt crediderunt quod hoc voca- 
bulum significet idem conjunctum vel divisum, sicut respub- 
lica apud nos. Sed hoc non est generaliter verum, immo in 
pluribus habet instantiam in omni lingua. Nam apud Hebraeos 
Is est vir, Ra videns, El Deus ; et ideo crediderunt multi 
quod hoc nomen patriarchae habet resolutionem in illa tria. 
Sed Hieronymus reprobat per multa argumenta ; quatuor 
enim possunt sumi e dictis suis a parte vocis, et quatuor vel 
quinque a parte rei. Nam in illis tribus nominibus aliae literae 
sunt et plures quam in nomine patriarchae, et aliter ordine et 
syllabicatae reperiuntur. Ex hoc ergo triplici argumento 
sumto penes literas concluditur per Hieronymum quod id 
significari non potest hinc inde ; cum potentia significationis 
ejusdem sumitur propter vocis identitatem, sed vocem et 
literas nimis variari, quum in nomine patriarchae sunt hae 
quinque literae per ordinem : lod, Sin, Resh, Aleph, Lamet, 
sicut ipsum Hebraeum hic positum declarat ^^^,, Israel. 
Sed in hoc triplici vocabulo hae octo literae habent hunc 
ordinem, scilicet, Aleph, lod, Sin, Resh, Aleph, He, Aleph, 
Lamet, ut hic Hebraeum ostendit, i^Sn^nb^K. Et quarto argui 
potest explicatione. Nam sicut puncta ostendunt nomen 
proprium non retinet apud Hebraeum sonum praecisum 
illorum vocabulorum. Nam secundum majorem quasi Iserael 
sonatur in quatuor syllabis, tamen ibi vocabulorum sonus in 
solis tribus syllabis coarctatur, quoniam punctum sub litera 



LINGUARUM COGNITIO. 83 

sonat i, et duo puncta sonant e, et linea cum puncto sub ea 
sonat a. Sed argumenta fortiora trahuntur ex sensu vocis 
secundum Hieronymum. Et hoc ostendit ipsum Hebraeum 
hic scriptum hoc modo : 

V T-: ^i §• VI ^ T «T !■ •• t: • • • »:• >'ti« •''ii- v - 

|T - 

Et textus Graecus habet sic : * quia invaluisti cum Domino [et 
cum hominibus valebis ^]/ 

Nam secundum Hieronymum et per textum Hebraeum, et 
Graecum, et Latinum, et per Josephum patet quod Israel non 
debct dici vir videns Deum, sed principalis vel princeps cum 
Deo, quoniam in Hebraeo ad literam est sic : * Et dixit Deus 
non vocabitur nomen tuum a modo Jacob, sed Israel ; quoniam 
principalis vel princeps fuisti cum Deo, et cum hominibus 
poteris principari.* Et ideo dicit Hieronymus quod sensus 
est, * Non vocabitur nomen tuum supplantator, hoc est Jacob, 
sed vocabitur nomen tuum princeps cum Deo, hoc est Israel. 
Quoniam ego princeps sum, sic tu, qui mecum luctari potuisti, 
princeps vocaberis. Si autem mecum pugnare invaluisti, 
quanto magis cum hominibus; hoc est, cum Esau, quem 
formidare non debes ^ ? ' Et quoque Latinum habet : * Quoniam 
si contra Dominum fuisti, quanto magis contra homines 
praevalebis ? ' Et Josephus primo antiquitatum libro, Israel 
ideo appellatum dicit, quia contra Angelum steterit. Omnia 
igitur haec, scilicet principari cum Deo, et invalescere, et 
fortem ess^, et stare cum Deo ut patet reducuntur ad 
eundem sensum, sed diversis vocabulis interpretationum, 
quorum nullum de virtute significationis suae potest elicere 
visionem Dei. Et ideo vera interpretatio est princeps cum 
Deo. Et adhuc confirmat hoc Hieronymus per argumentum 
derivationis ; nam Sarith et ab Israel nomine derivatur, et 
principem sonat Unde Sara uxor Abrahae princeps dicitur, 

' The words in brackets are omitted in the MSS. 

• See Jeroine*s Libtr Htbraicarum Qtnustionum in Genesim, Jerome adds : 
'Quamvis igitur grandis auctoritatis sint, et eloquentiae ipsorum umbra nos 
opprimat qui Israel virum sive meniem videniem deum transtulerunt, nos magis 
Scripturae et Angeli qui ipsum Israel vocavit auctoritate ducimur quam cujus- 
libet eloquentiae saecularis.' 

G 2 



84 OPERIS MAJORIS PARS TERTIA. 

ut dicit Hieronymus super septimum decimum capitulum 
Geneseos ; quapropter si vulgus vel aliqui antiqui, ut Eusebius 
Caesariensis in libro nominum Hebraeorum quem Hieronymus 
in Latinum vertit, et alii, famosa abutentes interpretatione 
dicunt Israel interpretari per virum videntem Deum^ dicamus 
cum Hieronymo^ IUud vero quod in libro Nominum inter- 
pretatur Israel Vir videns Deum omnium pene sermone de- 
cretum non tam vero quam violenter interpretatum videtur. 
Et igitur per Eusebium in libro Nominum quem Hieronymus 
transtulit in Latinum et per Ambrosium et alios forsitan 
sanctos allegare si quis concedat quod recta hujus vocabuli, 
Israel^ expositio sit Vir vidms Deum^ dicendum est quod locuti 
sunt secundam vulgatam expositionem, antequam veritas fuerit 
patefacta quam postea beatus Hieronymus vera et perfecta 
interpretatione Latinis rcvelavit, sicut in ejus libris continetur 
et in glosa etiam habetur. 

Et si forsan dicitur quod consuetudo vulgi theologorum 
modernorum hanc interpretationem frequentet, patet responsio 
per supradicta secundum Augustinum, et Cyprianum, et 
Isidorum, et alios et per varias declarationes ^ Nam secundum 
eos manifestatae veritati cedat consuetudo, et relicto errore 
vulgi sequamur veritatem. Et quod ex mera ignorantia venit 
non debet allegari, sicut accidit in proposito, et praecipue 
contra auctorem et doctorem sacrum non licet contraire, nisi 
pro se rationes sufficientes et auctoritates allegat Et ad om- 
nem afllirmationem poterit quilibet Hebraicae peritos consulere, 
et inveniet sententiam Hieronymi ratam et inconcussam^ 
Summa vero necessitas remediorum falsitatis requiritur in his 
interpretationibus propter formam Hebraei sermonis ; nam in 
interpretationibus vulgatis quae in fine bibliae ponuntur, sunt 
infinitae occasiones errorum : propter hoc erramus quod unum 
vocabulum aestimatur simplex secundum normam Latinorum, 
quod est multiplex apud Hebraeos: et abundantius erratur 
quod tali vocabulo dantur variae interpretationes tanquam 

' The remainder of the parag^ph is omitted in O. and is supplied from 
Jul. 

' et . . . declarationes om. in O. 
' Thb sentence omitted in O. 



LINGUARUM COGNITIO. 85 

ejusdem sint vocabuli Hebraei, cum tamen quaelibet sit diversi, 
eo quod vocabulum Hebraeum apud nos male consideratum in 
scriptura una habet diversas literas apud Hebraeos, penes quos 
recepit diversas interpretationes, secundum quod Hieronymus 
ponit exemplum in epistola de mansionibus. Nam oportet si 
ar scribatur per aUph, significat lumen ; si per ain, inimicum, si 
per heth^foramen ; per he^ montem ; dicit igitur quod vicesimo 
Numerorum quidam interpretati sunt his modis quatuor ; sed 
opiniones tres destruit, quia in Hebraeo scribitur hic per lie^ 
et ideo solum montem in hoc loco designat. Sed in prae- 
dicando et legendo theologi recurrunt ad omnes quatuor 
expositiones in hoc vocabulo, et sic alias^ igitur multipliciter 
errant. 

Est ultima ratio scientialis de necessitate linguarum, quod Latin 
Grammatica in lingua Latinorum tracta est a Graeco et|™J^^ 
Hebraeo. Nam litteras accepimus a Graecis, ut docet Pris- formed on 
cianus, et ^ totam rationem tractandi partes omnes Priscianus of^G^^eck 
accepit a Graecis et miscet Graecum in multa abundantia per *J^ 
omnes libros suos. Et ipsa vocabula linguae Latinae, et tam 
theologica quam phllosophica, ab alienis linguis pro parte 
maxima sunt transfusa, quorum aliqua suspicantur Latini esse 
alterius linguae; et de aliquibus non considerant quod ab 
aliena lingua descendunt Multa vero aestimantur quod sint 
penitus Latina, cum tamen sint Graeca, vel Hebraea, vel 
Chaldaea, seu Arabica, in quibus tam in pronunciatione quam 
in scriptura et sensu accidit multiplex error Latinonim ; nec 
est modicum errare in vocabulis, quia per consequens errabitur 
in orationibus, deinde in argumentis, tandem in his quae 
acstimantur concludi*. Nam Aristoteles dicit quod *qui 
nominum ignari sunt, saepe paralogizantur.' Et primum et 
principale fundamentum doctrinae ponit Boethius in certa et 
integra cognitione terminorum, sicut docet in libro de disci- 
plina scholarium, atque nos experimur hoc in singulis scientiis. 
Nam principalis difficultas * et utilitas est, quod homo sciat 
intelligere vocabula quae dicuntur in scientia et prudenter 

' The following six lines supplied by Jul., om. in O. 
' The last six words om. in O. 
3 difficultas et om. in O. 



86 OPERIS MAJORIS PARS TERTIA. 

sine errore proferre; quando veraciter scit hoc, potest per 
scriptum perficere sine ulteriori doctrina si sit diligens in 
studio. Nam textus scientiarum sunt ei plani, quando noverit 
proprie ac certe intelligere et interpretari ; et sine difficultate 
potest quemlibet sapientem intelligere, et cum quolibet suf- 
ficienter conferre, et a quolibet si necesse est edoceri. Et 
Aristoteles dicit in primo coeli et mundi, quod parvus error in 
principio est magnus in principiatis ; qui enim in fundamentis 
errat, necesse est ei in errore totum aedificium cumulare. 

Aestimamus igitur lingruam nostram Latinis dictionibus esse 
compositam, et pauca esse vocabula aliarum linguarum, cum 
tamen quae communiter utuntur sunt de linguis alienis, ut 
domus, scyphus, clericus, laicus, diabolus, Satanas^ ego, pater, 
mater, ambo, leo, ago, malum ^, et sic de infinitis, quae vix in 
magno volumine possunt congregari ; praecipue si scrutemur 
vocabula singularum scientiarum, et maxime theologiae et 
medicinae ; quo volumine nihil esset utilius, si vocabulorum 
omnium recta scriptura ac pronunciatio debita cum fideli 
derlvatione et recta interpretatione probarentur ^. Sed nunc in 
his quatuor erratur in magnum totius detrimentum sapientiae, 
qucd paucis exemplis potest intelligi. Nos enim non con- 
sidcramus ordinem linguarum, nec quod prior lingua non 
reccpit interpretationem posterioris, nec quod diversae linguae 
in eo quo diversae sunt non se mutuo exponunt : sed quod 
dicit Hieronymus, et maxime prior ex posteriori non potest 
originem habere, ut certum est omni homini rationem habenti ; 
unde Graecum non oritur ex Latino, nec Hebraeum ex Graeco, 
et non debet Hebraeum capere etymologiam ex Graeco, nec 
Graecum ex Latino : unde Hieronymus dicit contra quosdam 
in dicto loco memorato, quod Sara non Graecam sed Hebrai- 
cam debet habere rationem, Hebraea enim est. Et saepius 
dicit quod Lenaeus a X^qvq^ id est, lacus^ dicitur, non a lenio^ 
quia Graecum non potest Latinam etymblogiam recipere ; sed 
quod hcc facimus graviter et indifferenter. Et nos contra; 
nam dicimus quod amen^ licet sit Hebraeum, dicitur ab a, 
quod est sine^ et mejie Graeco, quod est defectus. Et cum 

^ The last nine examples om. in O. 

' J.*s reading, praeliarentur, is unintelligible. Jul. has probarentur. 



LINGUARUM COGNITIO. 87 

parasceue sit Graecum, dicimus quod derivatur a paro^ paras^ 
et coena, coenae, quae sunt Latina. Et ^ dicunt quod dogina 
dicitur a doceo^ et sic de infinitis quae omnia falsa sunt. Et non 
solum vulgus Latinorum sed auctores in his oberrant,et Hugo 
et ejus sectatores qui aestimant jubileum a jubilo derivari, 
cum tamen jubileutn debet esse Hebraeum. JubHo est 
Latinum ; sed non debet dici Jubileum ut litera i sit in 
secunda syllaba sicut in Jubilo, Debet i esse e litera ut 
dicatur jubclais^ sicut vult Isidorus et Papias, et omnes libri 
antiqui sic habent. Nam dicitur a jobel quod est Hebraeum. 
Ita aestimamus quod multa vocabula quae sunt in usu 
Latinorum debent exponi per alias linguas. 

Assueti autem in hoc credimus quod longe plura, quam Maov 
veritas sit,capiunt etymologiam aliunde. Nam sola illa voca- "^xSxi ° 
bula, quae oriuntur et derivantur ex Graeco et Hebraeo, ®"g^" , 

wroncly 

debent habere interpretationes per linguas illas. Ea enim, thought to 
quae pure Latina sunt, non possunt habere expositionem nisi ^ ^ore»gn. 
per vocabula Latina. Nam purum Latinum est omnino 
diversum ab omni lingua, et ideo non potest habere inter- 
pretationem aliunde : sed Latini non hoc considerant : imo 
indifferenter pura Latina per alias linguas interpretantur. 
Unde multis modis hoc verbum coelum quod est pure 
Latinum Graece interpretantur dicentes quod coelum dicitur 
quasi casa helios^ i.e. domus solis, nam sol dicitur helios ; 
sed incongrue dicunt et falso. Debent enim dicere, Casa 
heliu^ cum helios sit nominativi casus, heliu genitivi. Deinde 
falso dicitur. Nam sicut Varro peritissimus Latinorum et 
Plinius in prologo plene confirmat, coelum dicitur a coelo^ 
coelas, quod est scnlpo^ is^ quia stellis sculptum est et orna- 
tum. Quod etiam est lege scripturae vocabulorum. Nam 
coelo^ coelasy pro sculpo^ sculpis^ scribitur per diphthongum ae 
in omnibus libris antiquis. £t sic hoc verbum coelum apud 
omnes codices antiquos scribitur per diphthongum eandem. 
£t ideo derivatur a coelo quod est sculpo. £t ex hoc sequitur 
quod non derivatur a celo^ celas quod est occulto^ occulias, 
sicut illi qui huic nomini dant etymologiam absurdam dicentes 
sic dici quod occultatur et elongatur a nobis, vili errore sicut 

' The following passage, to the end of the paragraph, supplied from Jul. 



88 OPERIS MAJORIS PARS TERTIA. 

priores decepti. Similiter hoc nomen ave^ quod est pure 
Latinum, Graece exponunt, dicentes quod dicitur ab a^ quod 
est sim, et vey quasi sine ve: sed hoc fieri non debet, quia hoc 
vocabulum non sumitur a Graeco vocabulo cognatae stgni- 
ficationis. Nam chacre in Graeco signat ave in Latino, sed 
haec duo non concordant. Hic ergo est unus modus quo in 
infinitis Graecis vocabulis errat Latinus. 
Greek Alius modus est, quod in Graecis vocabulis non intelligimus 

m«aDd^^ eorum scripturam, quam habent multipliciter variatam ; quia 
stooti. vocabula consimilia in sono distinguunt in significato : unde 
habent triplex et duplcx o, et duplex t, ac p et c ; et habent 
undecim diphthongos, et multa alia, ut sic varietatem suorum 
vocabulorum in significando designent. Nam catos quod est 
inanis, a quo cenodoxia, i. e. inanis gloria, de quo Deutero- 
nomi septimo, per e breve scribitur. Et cenos quod est novus, 
a quo encenia, i. e. innovationes, ut nova festa et dedicationes, 
de quo Johannes decimo, et scribitur per ae diphthongum, sic 
caenos. Cenos vero quod communis, a quo cenobium et epi- 
cenium, scribitur per oi diphthongum, quam Latinus proferat 
e, sed deberet proferri i, ut diceret cinoSy unde ab hoc didtur 
cinomia, quod est secundum Hieronymum in correctione 
Psalterii, communis vel omnimoda musca. Unde Papias dicit 
quod scribitur per diphthongum in prima syllaba, sic coinomia. 
Et hoc manifestum est in Graeco Psalterio. Et cynos^ canis, qui 
scribitur per^ Graecum, unde cynomia^ i.e. musca canina, de qua 
Exodi octavo, et xenos per x^ quod est peregrinus, a quo xenia, 
quae sunt munera seu dona, de quibus liber Machabaeorum, 
et secundus Ecclesiastici. Et schenos ^&c sche est/unisj a quo 
schenobateSy qui graditur in fune et super funem. Scena est 
umbra, vel taberncu:ulum^ a quo scenopegia^ i. e. fixio tabemaculi, 
et scenofactoria ars est in qua Paulus Apostolus laborabat. 
Cum igitur derivativa istorum vocabulorum et composita 
sic variantur in significatis, licet sint similia in sermone 
et sono, manifestum est quod non est possibile evadere in 
sensu literali sine errore, qui non advertit scripturam hujus- 
modi. Unde magni viri et famosi expositores aliquando 
decepti sunt, sicut Rabanus, qui dicit quod scenofactoria ars 
docet facere funes^ quia aestimabat quod schenos^ quod est 



LINGUARUM COGNITIO. 89 

funis^ esset idem a quo nomen derivatur. Sed Beda docet 
contrarium volens quod a scena derivatur, et hoc manifestum 
est per scripturam vocabuli. Scilicet ^ ignoratione Actuum in 
Graeco textu scribitur vocabulum penultima syllaba sine 
aspiratione et per vocalem quae vocatur ita^ quod est i longum, 
et sic scribitur scena pro tabernaculo \ sed schenos pro fune 
scribitur per oe. diphthongum et per aspirationem. Et sic 
contentio est inter doctores de cinomia et de caeteris prae- 
dictis. Unde de xeniis credit vulgus quod nihil sit, et corri- 
gunt in textu Latino dicentes exenia. Sed in Bibliis antiquis 
non est sic, nec in Graeco ; nec potest sic dici secundum 
Graecam grammaticam quia oporteret quod ex praepositio 
Graeca poneretur primo quod non est possibile, quia vocabu- 
lum incipit per consonantem sicut patet per grammaticam 
Graecam. Per hunc modum accidit error quasi in infinitis 
vocabulis. 

Tertius modus est, quod licet Latini multum communicant Diflerences 
cum Graecis, tamen in aliquibus differant, quod non obser- ^^^ ^^j.. 
vatur ut oportet. Nam cum dicat Priscianus et omnes Latini mination 
sciunt, quod nomen arboris apud Ladnos est foeminini generis j^^ i^^tin. 
et terminatur in us, et nomen fructus est neutrius, et terminatur 
in um ; \xX.pomuSy pomum ; Pyrus, pyrum ; et sic de aliis, aesti- 
matur quod hoc sit intelligendum de omnibus vocabulis, quae 
sunt in usu Latinorum, ut de malo et de amygdalo et aliis. 
Nam regula Latinorum est solum intelligenda de Latinis 
dictionibus, non de Graeds nec aliis. Et quod hoc sit verum 
patet primo quod Latinus dat regulas de Latinis, et non 
pertinet ad eum ordinare regulas de linguis alienis. Deinde 
Priscianus dicit quod omne Graecum cadens in usum Lati- 
norum retinet genus suum quod habuit apud Graecos. Et 
ideo cum malum pro arbore sit Graecum et neutrius generis, est 
sic apud usum Latinorum. Et ideo tam pro fructu quam pro 
arbore est ejusdem generis et ejusdem terminationis. Et hoc 
probatur per Virgilium qui dicit in Georgicis mala insita arbores 
quae inservantur in fructus. Et super hoc Servius commentator 
qui fuit major quam Priscianus, cujus auctoritate saepius utitur, 
dicit, quod hoc, omne nomen arboris est foeminini generisy 
' This sentence, and the three foUowing, have been corrected from Jul. 



90 OPERIS MAJORIS PARS TERTIA. 

intelligendum est de Latinis, non de Graecis. Et certum est 
quod malutn est Graecum, licet secundum morem Latinorum 
aliquantulum sit aliter prolatum. Nulla dictio apud Graecos 
terminatur in m literam, sed in n ; et Latini omnes consue- 
verunt terminare dictiones suas in m, ut scammint, lignum^ 
pomum, et hujusoiodi. Idem multoties Latinus mutat ali- 
quam vocalem in vocabulo Graeco, ut ubi dicit Graecus 
grammaticosy Latinus dicit grammaticus^ et sic multipliciter ; 
et sic est hic. Nam Graecus dicit melon pro arbore et fructu, 
Latinus mutat e in a, sicut n in m, et dicit malum. Sed ista 
mutatio non mutat vocabulum secundum substantiam et 
secundum radicem, quia acceptum est a Graeco, licet ah'ter 
prolatum, et hoc omnes auctores testantur. Caeterum per 
textum Latinorum in antiquis libris, tam de theologia, quam 
de philosophia, invenitur semper malum pro arbore. Nam in 
primo Joel invenitur communiter apud omnes Biblias malum 
pro arbore, etiam usque correctores dimiserunt illud in novis 
Bibliis : et quarto Canticorum ubi dicitur, * sicut malum inter 
ligna sylvarum ' ; sic exponit Beda in originali, et duodecimo. 
Ecclesiastis est amygdalum et malogranatum in singulari et 
malogranata in plurali, quod non fieret, si malum non esset 
neutrius generis. Mutantur igitur hujusmodi vocabula se- 
cundum formam Latinorum. Et praecipue mirum est quod 
in aliquo correctores dimittunt antiquam literam et in alio 
abradunt, quod est omnino contra rationem. 
Mistakesin Similiter in pronunciatione literarum Graecarum multum 
due^to^ erratur, propter hoc, quod Latini volunt formani suam servare 
neglect in Graecis dictionibus ; et in hoc peccatur maxime, cum 
differ^«8. omnes Poetae et omnes antiqui Latini proferebant secundum 
primam institutionem. Sed nos moderni violavimus hoc 
multis modis contra usum omnium antiquorum ; verbi gratia, 
cum Priscianus dicit, quod nomina possessiva desinentia in 
nus longantur et acuuntur in penultima, ut Bovinus, Latinus, 
equinus, intelligenda est regula de Latinis dictionibus, non de 
Graecis, propter aliquas rationes tactas prius. Et ideo cum 
Adamantinum, Byssinum, Chrystallinum, Hyacinthinum, 
Bombycinum, Onychinum, Amethystinum, Smaragdinum, 
et hujus modi sunt Graeca, debent breviari in penultima, 



LINGUARUM COGNITIO. 91 

sicut Graeci faciunt. Praeterea nec ista simt possessiva. Nam 
duae tantum sunt terminationes possessivorum apud Graecos, 
scilicet in cos, ut Grammaticos; et in nios, ut Uranios, 
i. e. coelestis. Caeterum omnes Poetae Latini breviant penul- 
timam, et ideo non est poetica licentia quia communiter fit 
ab omnibus et ubicunque: quod enim raro fit et ex causa, 
licentiae poeticae ascribendum est, sed non quod fit semper et 
communiter. Unde Juvenalis, ^ amethystina convenit illiJ 
Et idem dicit, * Grandia tolluntur crystallina * ; penultimam 
corripiendo, sicut omnes faciunt, et nullus facit contrarium: 
igitur non est poetica licentia sed ex lege naturali. Et cum 
secundo Regum septimo decimo capitulo habeatur, 'siccaret 
ptisanas,' expositio famosa vocabulorum Bibliae, cui omnes 
adhaerent, nititur probare quod media sit producta ; et auctor 
illius expositionis defendit se per versum Horatii, 

*Tu cessas, agedum sume hoc ptisanarium orizae.' 
Sed error est, nam sicut per omnes auctores probatur, nun- 
quam abscinditur in metro, nisi una syllaba in fine dictionis ; 
et ideo sic debet scandi, * Ptisanari* orizae,' ut haec syllaba sa 
brevietur, et haec syllaba na longetur. Et hoc patet aliter, 
quia in omnibus derivativus a ante riupt longatur; ut con- 
trarium, armarium et hujusmodi infinita quae observantur in 
hac scansione, sed non modo vulgato cum dicitur ptisanar 
orizae ut duae syllabae auferantur, quia ibi breviatur haec 
syllaba na^ ut patet Ergo oportet quod media hujus dic- 
tionis ptisana sit brevis. Praeterea erratur in scriptura, nam 
in novis Bibliis habetur tipsanas quod nihil est, et debet 
p anteponi, sicut in hoc nomine Ptolemaeus. Et in hoc modo 
erratur infinities in aliis vocabulis, et tam violenter mutamus 
veras accidentium causas et regulas, quod non est remedium 
per magistros. Quoniam consuetudo cogit omnes male pro- 
ferre, ut in uno patet exemplo pro mille millibus. Butyrum 
habet penultimam correptam apud auctores ; unde Statius, 
*Lac tenerum cum melle bibit, butyrumque comedit' 
Et Macer in libro herbarum : 

*Cum butyro modicoque oleo decocta tumorem.' 
Et Graecus sic breviat. Atque componentia ipsum requirunt 
hoc. Nam componitur de tyros et bos^ ct tyros est breve in 



92 



OPERIS MAJORIS PARS TERTIA. 



(i) for ex- 
planation 
of liturgy, 



prima syllaba et est lacticinium, quod a bove venit. Sed 

longe sunt majores errores apud multos, et ignorantia veritatis 

apud omnes circa accentus. Sed major disputatio requiritur 

quam praesens scriptura concedit ^. 

^ Cum jam manifestavi quomodo cognitio linguarum sit 

necessaria Latinis propter studium sapientiae absolutum nunc 

volo declarare quomodo oportet eum haberi propter sapientiam 

Iraportance comparatam ad Dei Ecclesiam et rem publicam fidelium et 

to the f . ./.,,. . . 

church of confusionem mfidelium et eorum reprobationem qui converti 

stud^es^^ non possunt. Nam quadrupliciter in eis necessaria est eccle- 

siae, primo videlicet propter officium divinum, eo quod Graecis 

et Hebraeis et Chaldaeis utuntur in officio sicut in Scriptura. 

Et plura accipimus quorum Scriptura non facit usum, ut 

agios^ atheos^ athanatos^ iskiros^ yntas, eleisoUy et hujusmodi. 

Cum ergo ignoranius scripturam et pronuntiationem rectam et 

sensum multum deficimus a veritate et devotione psallendi. 

Nam loquimur sicut pica et psittacus et talia bruta animalia 

quae voces emittunt humanas, sed nec recte proferuntur nec 

intelliguntur quae dicuntur. Quum enim dicimus alleluia 

infinities in anno, deceret multum et expediret ut omnes per 

totam ecclesiam psallentes scirent quid sint duo vocabula, 

scilicet allelu et ia. Nam allelu significat idem quod Laudate^ 

et ia denotat Dominnm^ quum est unum de decem nominibus 

Dei, sicut Hieronymus scribit ad Marcellum ; et praecipue 

significat invisibilem, et Deus est maxime invisibilis. Verum 

non qubdcunque invisibile, sed Deum designat. Et cum in 

omni Missa dicimus Osanna, haec dictio est composita ex 

corrupto et integro. Nam ut Hieronymus dicit ad Damasum 

Papam, Os est idem quod Salvifica, et anna est indicatio depre- 

cantis, secundum quod per aleph scribitur syllaba prima; unde 

significat idem quod, salva deprecor. Nam aliter scribitur 

prima syllaba per e literam, et tunc significat conjunctionem 

quod Latinus sermo non habet. Et cum gloriosam Virginem 



* The subject of accentuation is treated with some fuUness in the Greek 
grammar by Bacon preserved in Corpus Christi College, Oxford ; and also in 
Compendium Studii, cap. xi (Brewer, pp. 508-514). 

* All that follows, to the end of Part III, is omitted in Jebb's edition, and 
has been restored here from Jul. 



LINGUARUM COGNITIO. 93 

salutamus, dicentes, Ave Maria gratia plena Dominus tecum, 
multum esset necessarium ad intellectum veracem et intellec- 
tum ut quilibet litteratus sciret sensum vocabuli ; et praecipue 
cum multi aestimantes scire in hoc oberrent. Mirum quidem 
vocabulum est Maron^ et significat dominum a quo venit 
Maria^ et idem est quod dominatrix, ut dicit Hieronymus in 
interpretationibus. Et hoc valde competit beatissimae Virgini, 
quae dominatur supra omnem immunditiam peccati expellen- 
dam a nobis et diabolicae fraudis et nequitiae, quia ipsa est 
terribilis peccato et de moribus sicut castrorum acies ordinata. 
Haec vero interpretatio est peritissima et sine calumnia. 
Dicit autem Hieronymus quod multi aestimaverunt interpretari 
.... quod ipse non recipit et dicit quod debet dici Stella 
Maris, vel amarum mare secundum Hebraicam interpreta- 
tionem. Et vere dicitur Stella Maris ut nos dirigat ad 
portum salutis, et Amarum Mare quia in omni paupertate et 
amaritudine temporali vixit in hoc mundo, et ipsius animam 
pertransivit gladio in morte Filii, ut sit nobis exemplum omnis 
patientiae et consolatrix in omnibus adversitatibus hujus 
mundi. Necesse est ergo nobis in omnibus psalmodiis et 
obsecrationibus nostris ut sciamus recte proponere et intelli- 
gere quaecunque et juxta verborum proprietatem devote 
nostras petitiones sonare, ut quod recte et devote petimus, 
Dei et sanctorum pietatem et merita ecclesiae consequamur. 
Sed hoc non possumus facere sine notitia vocabulorum alterius 
linguae. Et ideo multum expedit et necessarium est ut hoc 
sciamus. 

Secunda causa est quod Ecclesiae necessaria est cognitio (a) for ex- 
linguarum propter sacramenta et consecrationes. Nam ^[^^ra" 
intentio necessaria est sacramento, ut theologi sciunt. Et ments and 
intentionem praecedit intellectus et notitia rei faciendae. ^^*^' 
Et ideo per omnem modum expediret Ecclesiae ut sacerdotes 
et praelati omnia vocabula sacrificiorum et sacramentorum et 
consecrationum scirent recte proferre et intelligere, sicut 
a principio sacri et summi pontifices et omnes sancti 
patres et institutores ordinum ecclesiasticorum constituerunt 
ct sciverunt qualiter in verbis et sensibus mysteria Dei con- 
sisterent. Unde incipiendo a primis ut ab exorcismis et 



94 OPERIS MAJORIS PARS TERTIA. 

catharizationibus, et sic per baptismum et omnia sacramenta 
discurrendo, non solum decens sed expediens et necessaria cst 
ut ab eis qui ministrant sacramenta sciretur recta pronuntiatio 
et debitus intellectus, quatenus in nullo derogaretur sacramento. 
Sed modo per universam Ecclesiam innumerabiles proferunt 
verba instituta ab Ecclesia et nesciunt quod dicunt, nec ver- 
borum servant rectam pronuntiationcm, quod esse non potest 
sine injuria sacramenti. Utinam fiat cum plena efficacia 
effectus sacramentalis ! Et cum Ecclesia statuit hoc ex certa 
notitia, et omnes patres antiqui sciverunt rectam pronuntia- 
tionem et sensum vocabulorum secundum quod competebat 
sacramentis, nos nullam habemus excusationem ; sed turpis et 
vilis ignorantia est nulla tergiversatione excusanda. Et quum 
in consecrationibus ecclesiarum cuspide baculi pastoralis 
fuerint factae literae alterius linguae secundum ordinem 
alphabeti, certum est quod paucissimi faciunt figuras debitas 
secundum quod a sanctis patribus et Ecclesia fuerint institutae, 
propter ignorantiam characterarum alterius linguae. Et 
praecipue in hoc erratur quod tres figurae sunt quae nullo 
modo scribi deberent in Graeco alphabeto. Nam procul 
dubio figurae quae vocantur episemon, koppa, sanpi non sunt 
de alphabeto Graecorum, nec Graecis inservierunt in ordine 
literarum; sed sunt figurae et notae numerorum. Modo 
vero Latini non considerant quod Graeci numerant per literas 
alphabeti, et quod ad complendam computationem interserunt 
tres figuras prius nominatas, scilicet has ^, ^, "^. Sed hoc 
faciunt quum numerant, non quasi nominetur figura pro 
literis et scriptis. Unde in scribendo nunquam utuntur his 
tribus figuris nec ponunt eas in ordine alphabeti. Sed 
Ecclesia instituit quod literae solae alphabeti scriberentur in 
consecratione ecclesiae, et deceret uti literis non notis nume- 
rorum. Quapropter valde indignum est quod per universam 
Ecclesiam fiat hujus erronea scriptura. 

Et vile est quod haec nomina IHC, XPC, scribuntur per 
literas Graecas et aestimatur quod sunt Latinae, aut nescitur 
cujus modi sunt Graecae. Nam procul dubio in hoc nomine 
IHC prima est iota quae valet i nostrum ; secunda est ita, 
quae valet e longum. Tertia est sima quae valet s nostrum. 



LINGUARUM COGNITIO. 95 

Et in hoc nomine XPC,prima est chi quaevalet ch aspiratum. 
Secunda est ro quae valet r nostrum. Tertia est sima. 

Tertia vero causa est de notitia linguarum Ecclesiae Dei (3) for .<3ae 
necessaria. Nam multi Graeci et Chaldaei et Armeni et ©f foreign 
Syrii et Arabes et aliarum linguarum nationes subjiciuntur ^^^'^^' 
Ecclesiae Latinorum, cum quibus multa habet ordinare et 
illis varia mandare. Sed non possunt haec recte pertractari 
nec ut oportet utiliter nisi Latini sciant linguas earum. Cujus 
signum est quod omnes dictae nationes vacillant fide et 
moribus, et ordines ecclesiae salutares per sincerum non 
recipiunt in lingua materna. Unde accidit quod apud 
tales nationes sunt mali Christiani et ecclesia non regitur ut 
oportet. 

Quarta causa est propter totius Ecclesiae doctrinam a (4) for 
principio usque in finem dierum. Nam dicit Dominus, lota doctrin^ 
unum aut unum apex non peribit a lege donec omnia fiant. 
Et ideo docetur publice in h*bro de senibus Scripturarum quod 
singulae literae alphabeti Graeci figurabant super populum 
antiquum, et oportet numerum centenariorum annorum quibus 
decurrebat status illius gentis juxta singulas aetates et saecula 
[computare] secundum spirituales vires et potestates literarum. 
Et deinde .... ecclesiae Latinae per necessitates literarum 
Latinarum. Et consimilis est consideratio super ecclesia 
Graeca per literas sui alphabeti. Et in hujus consideratione 
mirabili tempora ponuntur secundum omnes status Ecclesiae 
usque in finem, et per quot centenarios annos durabit quae- 
libet immutatio quae accidet Ecclesiae in decursu suo, cui si 
prophetias et testimonia digna necteremus possemus per Dei 
gratiam praesentire utiliter ea quae Ecclesia recipiet tam in 
prosperis quam in adversis. Et ideo nil utilius esset hujus veri- 
tatis literarum consideratione et aliis considerationibus simi- 
libus. Nam ad certificationem harum rerum multae materiae 
requiruntur, quarum saltem una non ignobilis est per literas 
linguarum diversarum. Et nequeo satis admirari cum videatur 
inexpertis habere debile fundamentum, scilicet literas alpha- 
beti quae sunt prima puerorum rudimenta, sed secundum 
documentum apostoli munera sunt magis necessaria et majori 
honore circumdanda. Et sicut Deus clegit infirma ut fortia 



96 OPERIS MAJORIS PARS TERTIA. 

quaecumque confundat, ita in rebus quas reputamus minimas 
posuit majestas majora quam possit intelligere mens bumana. 
Et sic est in his literis triplicis alphabeti. Unde non sine 
maxima causa in epitaphio Domini scriptum est Hebraice 
Graece Latine, ut doceremur quod Ecclesia cruce Domini 
redempta habeat considerare veritates literarum triplicis. 
alphabeti; praecipue cum Ecclesia incepit in Hebraeis et 
profecit in Graecis et consummata est in Latinis. 
(5) fo' Quinto multum est necessaria reipublicae Latinorum diri- 

wUhfo^Sgn gendae cognitio linguarum propter tria. Unum est com- 
nations. meatio utilitatum necessariarum et mercatis et negotiis sine 
quibus Latini esse non possunt, quia medicina et omnia pre- 
tiosa recipiuntur ab aliis nationibus. Et inde oritur magnum 
malum Latinis et fraus eis infertur infinita quia linguas 
ignorant alienas, licet per interpretationes eloquantur. Nam 

hae raro sufficiunt. 

• •..••• 

Ex his ergo quae circa lingfuas dicta sunt patens est quod 
Latini magnum habent sapientiae detrimentum propter lin- 
guarum ignorantiam. Unde ex hac parte gloriari non possunt 
de sapientia ; immo multum inglorii et cum vario sapientiae 
damno languent. 



PARS QUARTA 
HUJUS PERSUASIONIS. 

In qua ostenditur potestas mathematicae in scientiis, et 
rebus, et occupationibus hujus mundi. 

DISTINCTIO PRIMA, 

HABENS CAPITULA TRIA. 

Capitulum I. 

Manifestato quod multae praeclarae radices sapientiae The key 
dependent ex potestate linguarum, per quas est introitus in ^J^ter 
sapientiam Latinorum, nunc volo revolvere fundamenta ejus- sciences is 
dem sapientiae penes scientias magnas, in quibus est specialis matic. 
potestas respectu caeterarum scientiarum et rerum hujus 
mundi. £t sunt quatuor scientiae magnae, sine quibus caeterae 
scientiae sciri non possunt, nec rerum notitia haberi : quibus 
scitis, potest quilibet gloriose proficere in sapientiae potestate 
sine difficultate et labore, non solum in scientiis humanis, 
sed divina. Et cujuslibet istarum tangetur virtus non solum 
propter sapientiam absolute, sed respectu caeterorum prae- 
dictonim. Et harum scientiarum porta et clavis est mathe- 
matica, quam sancti a principio mundi invenerunt, ut ostendam, 
et quae semper fuit in usu omnium sanctorum et sapientum 
prae omnibus aliis scientiis. Cujus negligentia jam per triginta 
vel quadraginta annos destruxit totum studium Latinorum. 
Quoniam qui ignorat eam non potest scire caeteras scientias 
nec res hujus mundi, ut probabo. Et, quod pejus est, homines 
eam ignorantes non percipiunt suam ignorantiam^ et ideo 
remedium non quaerunt. Ac per contrarium hujus scientiae 
notitia praeparat animum et elevat ad omnium certificatam 

VOL. I. H 



98 OPERIS MAJORIS PARS QUARTA. 

» 

cognitionem, ut si radices sapientiae datas circa illam cognoscat, 
et eas radices recte applicet ad caeterarum scientiarum et rerum 
cognitiones, tunc omnia sequentia poterit scire sine errore et 
sine dubitatione, ac de facili et potenter. Sine his enim nec 
praecedentia nec consequentia sciri possunt ; unde perficiunt 
priora et regulant, sicut finis ea quae sunt ad finem, et dis- 
ponunt et aperiunt viam ad sequentia. Ad quod nunc intendo 
innuere per auctorltatem et rationem ; et primo in scientiis 
humanis et rebus istius mundi, deinde in divina, et ultimo 
prout ad Ecclesiam et caetera tria comparantur. 

Capitulum II. 

In cuo probatur per auctoritatem, quod omnis scientia 
requirit mathematicam. 

Anthorities Per auctoritatem quidem sic procedo. Dicit Boetius^ in 
for thU secundo prologo Arithmeticae, quod ' mathematicae quatuor 
Boethius. partibus si careat inquisitor, verum minime invenire possit' 
Et iterum * Sine hac quidem speculatione veritatis nulli recte 
sapiendum est.' Et adhuc dicit * Qui spernit has semitas sapien- 
tiae, ei denuncio non recte philosophandum.' Et iterum, 
* Constat quisquis haec praetermiserit, omnis sapientiae perdi- 
disse doctrinam.' Quod etiam omnium virorum authenticorum 
sententia confirmat dicens, 'Inter omnes priscae auctoritatis 
viros, qui Pythagora duce puriore mentis ratione viguerunt, 
constare manifestum est, haud quemquam in philosophiae disci- 
plinis ad cumulum perfectionis evadere, nisi cui talis prudentiae 
nobilitas quodam quasi quadrivio investigatur.* Et in particulari 
ostenditur per Ptolemaeum et ipsum Boetium^. Cum enim 

* Boethius, as appears from a letter addresscd to him by Theodoric which 
is quoted by Cassiodorus, made Latin translations of many of the Greek mathe- 
maticians ; Euclid, Nicomachus, Archimedes, Ptolemy, &c. These, however. 
have disappeared ; the two books De Instiiutiofu Arithmetica, and the five 
books De Musicay with a few doubtful fragments of his Gtometry, alone remain. 
The expression quadrivium, as applied to the four sciences of arithmetic, 
music, geometry, and astronomy, seems to have originated with Boethius. 

' In the introduction to the Almagest Ptolemy remarks that mathematic holds 
an intermediate phice between the invisible and incomprehensible object of 



MATHEMATICAE IN PHYSICIS UTILITAS, 99 

sint modi tres philosophiae essentiales, ut dicit Aristoteles 
in sexto Metaphysicae, mathematicus, naturalis, et divinus, non 
parum valet mathematicus ad reliquorum duorum modorum 
scientiae comprehensionem, ut docet Ptolemaeus in capitulo Ptolemy. 
primo Almagesti quod et ipse ibidem ostendit. Et cum divinus 
sit dupliciter, ut patet ex primo Metaphysicae, scilicet Philoso- 
phia prima, quae Deum esse ostendit, cujus proprietatesexcelsas 
investigat, et civilis scientia quae cultum divinum statuit, 
multaque de eo secundum possibilitatem hominis exponit, ad 
utramque istarum multum valere mathematicam idem Ptole- 
meus asserit et declarat Unde Boetius in fine arithmcticae 
mathematicas medietates asserit in rebus civilibus inveniri. 
Dicit enim quod * arithmetica medietas reipublicae comparatur 
quae a paucis r^itur, idcirco quod in minoribus ejus terminis 
major proportio fit, musicam vero medietatem optimatum 
dicit esse rempublicam. eo quod in majoribus terminis major 
proportionalitas invenitur. Geometrica medietas popularis 
quodammodo exaequatae civitatis est : namque vel in minoribus 
vel in majoribus aequali omnium proportionalitate componun- 
tur. Est enim inter omnes paritas quaedam medietatis aequum 
jus in proportionibus conservantis.' Et quod sine hisrespublica 
regi non potest, Aristoteles et ejus expositores in moralibus in 
pluribus locis docent. De his vero medietatibus exponetur, 
quando ad divinas veritates applicabuntur. Cum vero omnes 
modi Philosophiae essentiales, qui sunt plures quam quadra- 
ginta scientiae ad invicem distinctae, reducantur ad hos tres, 
sufficit nunc per auctoritates dictas persuasum esse valorem 
mathematicae respectu modorum philosophiae essentialium. 

Modi autem philosophiae accidentales sunt grammatica et Alphar- 
logica. Et quod sine mathematica non possunt sciri scientiae prow 
istac patet per Alpharabium in libro de scientiis. Nam etsi dependence 

. . . . ofgTanuiiar 

grammatica puens mmistrat ea quae vocis sunt et proprietates and oflogic 

on mathe* 
Theology, and the ahiftin|!f phenomena of nature. Td iilv ^CXAa ^ yiwri rou ™^^^ 
BwpftiTueod fiaXko» &v ns ilttaoiaM f MarAXr/ifftw crroi* r6 filv 0€o\oyuc6p Stfll t6 
warT^X&s A^ayls abrov koI drcWXijrror, t6 52 ^vouc^ Sid rd rrjt (fXrfs dotaToy koI 
d8i;Xor* &s 9tiL tovto lafiktoTt Ar Iktioai wfH alT&v diunfo^ooi Tobs ^Xooo^owras' 
ft6»ov 9k t6 /taBfiiMaTuc6y, (t tis k^tToOTUCws o^r^ wpooipx^'''^ fitfiaiay Mol d/icrd» 
wioroy Tois iuTax*'poiUyoiS r^ ttHrioty wap&ox^- ^e indicates also the value 
of mathematical study in elevating and consolidating character. 

H 2 



loo OPERIS MAJORIS PARS QUARTA. 

ejus in prosa, et metro, et rhythmo, nihilominus tamen hoc facit 
pueriliter^ et per viam narrationis, non per causas, nec per 
rationes. Nam alterius scientiae est dare causas horum, 
scilicet illius, quae vocum naturam plenarie habet considerare, 
et haec sola est musica, cujus species et partes multae sunt. 
Nam una est prosaica, et altera est metrica et tertia est 
rhythmica, et quarta est melica in cantu. Et praeter has 
habet plures. Et prosaica docet causas omnium elevationum 
vocum in prosa, secundum accentuum difierentias et secundum 
cola et commata et periodos et hujusmodi ^. Et metrica docet 
omnes rationes et causas pedum et metrorum. Et rhythmica 
de omni modulatione et proportione suavi rhythmorum docet, 
quia omnia ista sunt quaedam genera cantus, licet non sic ut 
in cantu usuali. Nam accentus dicitur quasi accantus, de 
accino^ accinis, Unde ad musicam pertinent sicut docet 
Cassiodorus in musica, et Censorinus in libris de accentu, et 
sic de aliis. Hoc autem testantur auctores musicae, et libri 
de illa scientia. Et his concordat Alpharabius in libro de 
divisione scientiarum. Ergo grammatica dependet causaliter 
ex musica. 

Eodem modo logica. Nam finis logicae est compositio 
argumentorum quae movent intellectum practicum ad iidem 
et amorem virtutis et felicitatis futurae, ut prius ostensum 
est, quae argumenta traduntur in libris Aristotelis de his argu- 
mentis, ut declaratum est. Sed haec argumenta debent esse 
in fine pulchritudinis, ut rapiatur animus hominis ad salutiferas 
veritates subito et sine praevisione, ut docetur in illis libris. 
Et Alpharabius * hoc docet maxime de poetico, cujus sermones 

^ For a fuller discussion of punctuation, metre, and rhythm, see OpHS 
Tertium, ch. 69 and 63. 

' Abu Nasr Muhammed ibn Muhammed ben Tarch&n ben Auzelag el F&rabi, 
known in the Western world as Alpharabius, was born a. d. 870 in the town 
of Farab (afterwards called Otrar) in Turkestan, and is one of many instances 
proving that Mahommedan learning in the Middle Ages was not limited to the 
Arab race. He was ignorant of Arabic tili he came to Bagdad for the purposes 
of study. Having acquired it he became one of the most zealous students of 
Aristotle, devoting himself specially to the Physics and the De Amma. The 
latter part of his life was spent in Damascus, where he died in 950 a. d. Of 
his original works the most important was Liber de scientiis tammque numero 
pariibHS ei pra€stantia» This work was translated by Dominicus Gundisalvi, at 



MATHEMATICAE IN PHYSICIS UTILITAS. loi 

debent essc sublimes et dccori, et ideo cum ornatu prosaico, 
et metrico, et rhythmico insigniti, secundum quod competit 
loco et tempori et personis et materiae de qua sit persuasio. 
Et sic docuit Aristoteles in libro suo de poetico argfumento, 
quem non ausus fuit interpres Hermannus transferre in Latinum 
propter metrorum difficultatem, quam non intellexit, ut ipse 
dicit in prologo commentarii Averrois super illum librum. Et 
ideo finis logicae pendet ex musica. Sed finis est nobilissimum 
in re, et imponit necessitatem eis quae sunt ad finem, ut Ari- 
stoteles dicit in secundo Physicae ; nec habent utilitatem suam 
ea quae naturaliter ordinantur ad finem, nisi quando ad finem 
suum comparantur, ut patet in singulis. Et ideo tota utilitas 
logicae nascitur ex comparatione logicalium omnium ad hujus- 
modi argumenta, et ideo cum dependeant ex musicalibus 
necesse est logicam mendicare potestatem musicae. Et haec 

Toledo, in the twelflth century. In the following century Hermannus Ale- 
mannus translated Aristot]e's Rhetoric from the Arabic, and with it certain 
commentaries of Alpharabius. ' Omnia enim,' he says, 'in glosa super hunc 
libruro exquisite Alfarabius pertractavit' Hermann observes, however, that 
'Alfarabius multa exempla Graeca propter ipsorum obscuritatem pertransiens 
derelinquit' The Arabic version of Aristotle^s Poetics seems to have been 
made not by Alfarabius but by Averroes. Hermann remarks on the extreme 
difficulty of rendering this version into Latin, ^ propter disconvenicntiam modi 
metrificandi in Graeco cum modo metrificandi in Arabico, et propter vocabulorum 
obscuritatem, et plures alias causas.' 

Alpharabins is one of the authors (Aristotle, Avicenna, and Algazel being the 
others) from whom David the Jew compiled the work De Causis, of which 
Albertus Magnus gives a long description, and which is cited both by Bacon 
and by Thomas Aquinas. See Jourdain, pp. iia, 138-145, 184-5; ^so 
Wuestenfeld, GeschichU dcr Arabischen AerzU und Naturforschtr (GOttingen, 
1840). 

The short treatise, De ScienHis^ is interesting for its comprehensive and 
encydopaedic survey of Science. It consists of five chaptecs. i. De Scientia 
Linguae et partibus ejus. a. De Scientia Logicae et partibus ejus. 3. De 
Scientiis doctrinalibus, quae sunt Geometria, Arithmetica, Sdentia de Aspec- 
tibus, Scientia stellarum doctrinalis, Sdentia Musicae, Scientia de Ponderibus, 
Scientia de Ingeniis. 4. De Scientia naturali et partibus ejus; et Sdentia 
divina et partibus ejus. 5. De Sdentia dvili et partibus ejus, et de Scientia 
judicandi, et de Scientia eloquendi. 

Like Bacon, Alfarabi includes rhetoric and poetic as parts of Logic. ' Rhe- 
torica movet animum auditoris et indinat ad illud quod voluerit, ut credatur id 
quod didt et generet in eo cognitionem proximam certitudini. Proprium est 
autem Poeticae sermonibus sensum facere imaginari pulcnim aliquid et dubium 
quod non est, iu ut auditor credat et aliquid abhorreat vel appeUt . . . quoniam 
Imaginatio plus operatur in homine quam scientia vel cognitio.' 



loa OPERIS MAJORIS PARS QUARTA. 

omnia sunt secundum sententiam Alpharabii in libro de 
scientiis, et patent similiter per Aristotelem et Averroem in 
libris suis, licet Latini horum usum non habeant. Sed non 
solum dependet cognitio logicae a mathematica propter suum 
finem, sed propter medium et cor ejus, quod est liber pos- 
teriorum, nam ille libcr docet artcm demonstrandi. Sed nec 
principia demonstrationisj nec conclusiones, nec ipsa tota 
potest cognosci, nec manifestari nisi in mathematicis rebus, 
quia ibi solum est demonstratio vera et potens, ut omnes sciunt 
et exponetur post. Quapropter necesse est logicam a mathe- 
maticis dependere. 
Without Item propter suum principium, non solum propter medium 
matic^the ^^ finem. Nam liber praedicamentorum est primus liber 
Catcgories lc^icae secundum Aristotelem. Sed constat praedicamentum 
inteUigible. quantitatis cognosci non posse sine mathematica. Nam sola 
mathematica constituitur de quantitate cog^oscenda Quan- 
titati vero annexa sunt praedicamenta de quando et ubi. Nam 
quando attinet tempori, et ubi oritur ex loco. Praedicamentum 
habitus non potest cognosci sine praedicamento ubi, ut docet 
Averroes in quinto Metaphysicae. Major vero pars praedica- 
menti qualitatis continet passiones et proprietates quantitatum, 
quia omnia quae sunt in quarto genere qualitatis vocantur quali- 
tates in quantitatibus Et omnes passiones earum quae absolute 
debentur eis sunt qualitates, de quibus magna pars geometriae 
et arithmeticae constituuntur, sicut sunt rectum et curvum, et 
caetera quae lineae debentur, et triangulatio et omnis reliqua 
figuratio, quae superficiei et corpori assignantur; et primum 
incompositum in numeris, ut docet Aristoteles quinto Meta- 
physicae et caeterae passiones numerorum absolutae. Quicquid 
autem dignum est consideratione in praedicamento relationis 
est proprietas quantitatis, ut sunt proportiones et proportion- 
alitates, et medietates geometricae, et arithmeticae, et musicac, 
ct species majoris inaequalitatis et minoris. Substantiae vero 
spirituales non cognoscuntur per philosophiam nisi per cor- 
porales, et maxime supercoelestes, secundum quod Aristoteles 
docet undecimo Metaphysicae. Nec inferiora cognoscuntur 
nisi per superiora, quia coelestia sunt causae inferiorum. Sed 
coelestia non cognoscuntur nisi per quantitatem, sicut patet 



MATHEMATICAE IN PHYSICIS UTILITAS, 103 

ex astronomia. Et ideb omnia praedicamenta dcpendent ex 
cognitione quantitatis, de qua est mathematica, et ideo virtus 
tota logicae dependet ex mathematica. 



Capitulum III. 

In quo probatur per rationem quod omnis scientia requirit Mathe- 
mathematicam. maticai 

examplcs 
nsed to 

Quod vero per auctoritatem de tota mathematica ostensum ^"^*J"^® 
est, potest nunc per rationem similiter ostendi. £t primo, sciences. 
quia aliae scientiae utuntur exemplis mathematicis, sed 
exempla ponuntur propter evidentiam rerum de quibus 
scientiae constituuntur ; quare ignoratis exemplis, ignorantur 
ea propter quorum intelligentiam adducuntur. Cum enim 
alteratio in naturalibus non inveniatur sine augmento et 
diminutione quibuscunque nec haec sine alteratione: non 
potuit Aristoteles ad purum manifestare differentiam inter 
augmentum et alterationem per aliquod exemplum naturale, 
quia semper concomitantur se aliquo modo; propter quod 
posuit exemplum mathematicum in quadrang^lo quod addito 
gnomone crevit, ct non alteratur. Quod exemplum ante 
vigesimam secundam propositionem sexti libri elementorum 
non potest intelligi. In iila enim sexti probatur, quod 
quadrangulus minor est omnino similis majori. £t ideo non 
alteratur minor, cum fiat major de minore per gnomonis 
additionem. 

Secundo, quia mathematicarum rerum cognitio est quasi Com- 
nobis innata. Socrati enim interrogianti geometrica a puero ormaShe" 
pusione, ut recitat Tuliius primo Tusculanarum quaestionum matical 
ita respondebat, quasi geometriam didicisset £t hoc saepe innate. 
expertum est in multis ; quod non accidit in aliis scientiis, ut 
ex sequentibus magis erit manife^tum. Quapropter cum sit 
quasi innata, et tanquam praecedens inventionem et doctrinam, 
seu saltem minus indigens eis quam aliae scientiae, prima erit 
inter scientias et praecedens alias^ disponens nos ad eas ; 
quoniam quae innata sunt vel prope disponunt ad acquisita. 

Tertio, quia haec scientia prius est inter omnes partes 



I04 OPERIS MAJORIS PARS QUARTA. 

Eariicst phUosophiae inventa. A principio enim humani generis haec 
discovered. prjino inventa est. Quoniam ante diluvium et post, per filios 
Adae, et per Noe et filios ejus, sicut ex prologo compositionis 
astrolabii secundum Ptolemaeum, et ex Albumazar in majori 
introductorio astronomiae, et ex primo antiquitatum libro 
manifcstum est, et hoc quantum ad omnes ejus partes^ 
scilicet geometriam, arithmeticam, musicam, astronomiam. 
Illud autem non contigisset, nisi quia haec scientia est prior 
aliis, et naturaliter eas praecedens. Quare manifestum est, 
quod haec debet primo sciri, ut per eam promoveamur ad 
omnes scientias posteriores. 
iiasiestof Quarto, quia nobis est nata via a facih*bus ad difficilia. 
8Km^^*" Sed haec scientia est facillima. Quod manifestum est in eo, 
quod non refugit intellectum alicujus. Laici enim et omnino 
illiterati figurare et computare sciunt, et cantare, et haec sunt 
opera mathematicae. Sed primo incipiendum est ab his quae 
sint communia laicis et literatis ; et non solum damnosum est 
clericis, sed omnino turpe et vile, quod ipsi ignorant quod laici 
Accessible utiliter et pulchre sciunt. Quinto videmus quod clerici licet 
Ihiilcst. nidissimi mathematicalia possunt scire, quamvis ad alias 
scientias non valeant attingere. Insuper semel et bis 
audiendo plus homo de ea potest cognoscere certo et veraciter 
sine errore, quam decies de aliis partibus philosophiae, ut 
The first patet experienti. Sexto, quoniam nata est nobis via ab his 
tcachSig. ^"^^ conveniunt statui et ingenio puerili, quia pueri a nobis 
notioribus et primo addiscendis incipiunt Sed hujusmodi est 
mathematica, quoniam primo docentur canere^ et eodem modo 
possunt capere modum figurandi et numerandi, et longe 
facilius et necesse esset eis scire de numeris ante cantum ; quia 
in proportionibus numerorum tota ratio numeri exemplariter 
explicatur, sicut auctores musicae docent, tam in ecclesiastica 
musica^ quam in philosophica. Sed ratio numerorum a figuris 
dependet, quia numeri hneares, et superficialcs, et corporales, 
et quadrati, et cubici, et pentagoni et hexagoni, et caeteri, 
a lineis et figuris et angulis cognoscuntur. Expertum enim 
est, quod pueri melius et dtius addiscunt mathematicalia, ut 
manifestum est in cantu, et etiam per experientiam scimus, 
quod pueri melius addiscunt et capiunt mathematicalia, quam 



MATHEMATICAE IN PHYSICIS UTILITAS. 105 

alias partes philosophiae. Nam Aristoteles dicit in sexto 
Ethicorum quod juvenes possunt cito scire mathematicalia, non 
sic naturalia, nec metaphysicalia, nec moralia. Quare dis- 
ponendus est animus prius per haec quam per alia. 

Septimo, ubi non sunt eadem nobis nota et naturae, nata it leads 
est nobis via a notioribus nobis ad notiora naturae. Sivej^^^l"^ 
simpliciter et facilius scimus ea, quae nobis notiora sunt, et «s to things 
cum magna difficultate devenimus in ea, quae sunt notiora natore. 
naturae. Et nota naturae sunt male et imperfecte nobis 
cognita, quia intellectus noster se habet ad ea, quae sunt sic 
manifesta naturae, sicut oculus vespertilionis ad lucem solis, ut 
vult Aristoteles secundoMetaphysicae ; sicut sunt maxime Deus 
et angeli, et vita futura et coelestia, et aliae creaturae nobili- 
ores aliis. quia quanto sunt nobiliores, tanto sunt nobis minus 
notae. Et haec vocantur nota naturae. et simpiiciter. Ergo 
per oppositum ubi eadem sunt nota nobis et naturae, multum 
proficimus circa nota naturae, et omnia quae ibi sunt, et ad ea 
possumus attingere ut sciamus ea perfecte. Sed in mathe- 
matica tantum, ut dicit Averroes ^ primo physicae et septimo 
metaphysico et super tertio coeli et mundi, sunt eadem nobis 
nota et naturae sive simpliciter. Ei^o sicut in mathematica 
ad ea quae sunt nobis nota complete attingimus, sic ad ea 
quae sunt nota naturae et simpliciter. Quare ad intima illius 
scientiae possumus simpliciter attingere. Cum ergo hoc non 
valeamus in aliis, manifestum est quod haec est magis nota. 
Quapropter ab ea sumenda est origo nostrae cognitionis. 

Item octavo, quia omne dubium fit notum per certum, et Itisthe 
omnis error evacuatur per solidam veritatem. Sed in mathe- 2^ ' 
matica possumus devenire ad plenam veritatem sine errore, et 
ad omnium certitudinem sine dubitatione : quoniam in ea 
convenit haberi demonstrationem per causam propriam et 
necesisariam. Et demonstratio facit cognosci veritatem. £t 
similiter in ea contingit haberi ad omnia exemplum sensibile, 
et experientiam sensibilem figurando et numerando, ut omnia 

' In his commentary on the first book of De Natur. Auscult.^ Averroes sa^rs, 
' lUa quae sunt cognita apud nos in rebus naturalibus non sunt illa quae sunt 
cognita simpliciter, id est, naturaliter. Quod est contrarium in mathematicis : 
illa enim quae sunt cognita in illis simpHciter, et sunt causae priores in esse, 
sunt cognita apud nos.' 



io6 OPERIS MAJORIS PARS QUARTA. 

ad sensum manifestentur : propter quod non potest esse 
dubitatio in ea. Std in aliis scientiis excluso mathematicae 
beneficio, tot sunt dubitationes, tot opiniones, tot errores 
a parte hominis, ut non possint explicari^ ut manifestum est, 
quoniam demonstratio per causam propriam et necessariam 
non est in eis ex propria potestate, eo quod in naturalibus 
propter generationem et corruptionem propriarum causarum, 
sicut effectuum, non est necessitas. In metaphysicis non potest 
fieri demonstratio nisi per eifectum. Quoniam inveniuntur 
spiritualia per corporales effectus et creator per creaturam, 
sicut patet in illa scientia. In moralibus non possunt esse 
ex propriis demonstrationes, ut Aristoteles docet. Et similiter 
nec in logicalibus nec grammaticalibus, ut planum est, possunt 
^sst demonstrationes potissimae propter debilitatem materiae 
de qua sunt illae scientiae. £t ideo in sola mathematica sunt 
demonstrationes potissimae |>er causam necessariam. £t ideo 
solum ibi potest homo ex potestate illius scientiae devenire ad 
veritatem. Similiter in aliis scientiis sunt dubitationes, et 
opiniones, et contrarietates a parte nostra, ut vix concordetur 
in una vilissima quaestione, nec in uno sophismate ; non enim 
sunt in eis ex sua proprietate experientiae figurationum et 
numerationum, per quas omnia certificari debent. £t ideo in 
sola mathematica est certitudo sine dubitatione. 

Quare patet quod si in aliis scientiis debemus venire in 
certitudinem sine dubitatione et ad veritatem sine errore, 
oportet ut fundamenta cognitionis in mathematica ponamus ; 
quatenus per eam dispositi possumus pertingere ad certitu- 
dinem aliarum scientiarum, et ad veritatcm per exclusionem 
erroris. £t haec ratio potest per simiie magis manifestari, et 
principale etiam propositum nonum £uclidis. Sicut enim 
cognitio conclusionis se habet ad cognitionem praemissarum, 
ut si sit in eis error et dubitatio, non possit veritas haberi per 
eas de conclusione, nec certitudo, quia dubium non certificatur 
per dubium, nec verum per falsum probatur, licet possit 
syllogizari ex falsis, syllogismo inferente non probante; sic 
est de scientiis totalibus, quod illae in quibus sunt dubitationes 
vehementes et multiplices, atque opiniones et errores, dico 
saltem a parte nostra, oportet quod hujusmodi dubitationes et 



MATHEMATICAE IN PHYSICIS UTIUTAS. 107 

falsitates evacuentur per aliquam scientiam nobis certam, et in 
qua nec dubitamus nec erramus. Cum enim conclusiones et 
principia propria cis sint partes totalium scientiarum, sicut 
pars se habet ad partem, ut condusio ad praemissas, sic 
scientia ad scientiam, ut scilicet scientia, quae est plena 
dubitationibus et opinionibus respersa atque obscuritatibus, 
non valeat certificari, nec manifestari, nec verificari, nisi per 
aliam scientiam notam et verificatam, et nobis certam et 
planam, sicut est de conclusione per praemissas. Sed sola 
mathematica, ut prius habitum est, manet nobis certa et 
verificata in fine certitudinis et verificationis. Quapropter 
per hanc oportet omnes alias scientias sciri et certificari. 

Et quoniam jam per proprietatem istius scientiae ostensum Considera- 
est, quod mathematica est prior aliis, et eis utilis et necessaria, subject- 
nunc ostenditur hoc per rationes sumptas a parte sui subjecti. ™a"er of 
£t primo sic, quia nobis est via nata a sensu ad inteliectum, matics 
quoniam deficiente sensu deficit scientia quae est secundum J^^^V** 
illumsensum^ut diciturprimoPosteriorum,quoniamsecundum conclnsion, 
quod proficit sensus, proficit humanus intellectus. Sed quan- 
titas est maxime sensibilis, quia est sensibile commune, et ab 
aliis sensibus sentitur, et nihil potest sentiri sine quantitate 
quapropter maxime potest intellectus proficere circa quanti- 
tatem. Secundo, quia ii>se actus intelligendi secundum se 
ipsum non perficitur sine quantitate continua, quia dicit 
Aristoteles in libro de Memoria^ et Reminiscentia quod omnis 
intellectus noster est cum continuo et tempore. Unde quanta 
et corpora intelligimus intuitu intellectus, quia species eorum 
apud intellectum sunt. Incorporeorum autem species non sic 
recipiuntur intellectu nostro; aut si fiant in eo, secundum 
quod Avicenna dicit tcrtio Metaphysicorum, non tamen hoc 
percipimus propter occupationem fortiorem intellectus nostri 
circa corpora et quanta. £t ideo per viam argumentationis 
et admirationis corporalium et quantorum investigamus 
rerum incorporalium notitiam, sicut Aristoteles facit in libro 

^ ^aftp^ 9k Kid in tt rts afor^tfit iKKiXMwtv drdymf koI kwnrriiiaiv nv^ ««AcXoi- 
viimu Anafyt. Post. i 18. 

' Oitc Mix*f^ potty o^iv &vfv rw irwtxovSf oW dvtv xp^*^ ^^ 1*4 ^* XR^V 
&rra, D$ Memoria, cap. i. 



io8 OPERIS MAJORIS PARS QUARTA. 

undecimo Metaphysicorum. Quapropter proficiet maxime 
intellectus circa ipsam quantitatem, eo quod quanta et corpora 
in quantum hujusmodi appropriantur intellectui humano 
secundum statum communem intelligendi. Unumquodque 
est propter quod et illud magis. 
in which ^j omnem autem confirmationem potest ratio ultima sumi 

wise men . . *^ . . . 

ofallages ex experientia sapientum ; nam omnes sapientes antiqui 
concur. laborarunt in mathematica, ut omnia scirent, sicut nos vidimus 
de aliquibus nostri temporis, et audivimus de aliis, qui per 
mathematicam, quam bene sciverunt, omnem scientiam cog- 
noverunt Inventi enim sunt viri famosissimi, ut Episcopus 
Robertus Lincolniensis, et Frater Adam de Marisco, ct multi 
alii, qui per potestatem mathematicae sciverunt causas omnium 
exph'care, et tam humana quam divina sufiicienter exponere. 
Hujus autem rei certitudo patet in scriptis illorum virorum, 
ut de impressionibus, sicut de iride et de cometis, et de 
generatione caloris, et locorum mundi investigatione, et de 
coelestibus et aliis, quibus tam theologia quam philosophia 
utitur. Quapropter manifestum est quod mathematica est 
omnino necessaria et utilis aliis scientiis. 

Hae rationes sunt universales, sed in particulari contingit 
hoc ostendi descendendo ad omnes partes philosophiae, quo- 
modo per applicationem mathematicae sciuntur omnia. £t 
hoc nihil aliud est, quam ostendere scientias ah'as non debere 
sciri per argumenta dialectica et sophistica quae introducuntur 
communiter, sed per demonstrationes mathematicas descen- 
dentes in veritates et opera aliarum scientiarum et regulantes 
eas, sine quibus nec possunt intelligi, nec manifestari, nec 
doceri, nec disci. Si quis vero in particuiari descenderet 
applicando mathematicae potestatem ad singulas sdentias, 
viderit quod nihil in eis posset sciri magnificum sine mathe- 
matica. Sed hoc nihil aliud esset, nisi constituere tractatus 
certos de omnibus scientiis, et pervias mathematicae verificare 
omnia quae scientiis caeteris sunt necessaria. Sed hoc non 
est praesentis speculationis. 



MATHEMATICAE IN PHYSICIS UTILITAS. 109 



DISTINCTIO SECUNDA. 

In qua ostenditur, quod res hujus mundi requirunt mathe- 
maticam, habens capitula tria. 

Capitulum I. 

In primo docetur in universali quod coelestia et inferiora 
requirunt mathematicam. 

Quod de scientiis jam ostensum est, potest de rebus mani- In the 
festari. Nam impossibile est res hujus mundi sciri, nisi sciatur ^e^^wns 
mathematica. De coelestibus enim certum est omnibus, quia theneed 
duae scientiae magnae mathematicae sunt de eis, scilicet niatics is 
astrologia speculativa, et astrolog^ia practica. Prima specu- obvious. 
latur quantitates omnium quae sunt in coelestibus, et omnia 
quae ad quantitatem reducuntur, tam discretam quam con- 
tinuam quantitatem. Nam numerum coelorum et stellarum, 
quarum quantitas potest per instrumenta comprehendi, certi- 
ficat, et figuras omnium, et magnitudines et aititudines a 
terra ac spissitudines et numerum ac magnitudinem ac parvi- 
tatem, ortum et occasum signorum stellarum, et motum tam 
coelorum quam stellarum, et quantitates et varietates eclip- 
sium. Item descendit ad quantitatem et figuram habitabilis, 
et omnium partium ejus magnarum, quae vocantur climata, 
et ostendit diversitatem horizontium et dierum ac noctium 
secundum singula climata. Haec ergo determinantur hic, et 
multa eis annexa. Practica vero descendit ad hoc, ut ad 
onmem horam sciamus loca pianetarum et stellarum, et 
aspectus et compositiones earum et omnia quae in coelestibus 
renovantur, atque descendit ad ea quae fiunt in aere, cujus- 
modi sunt cometae, et irides, et caetera ibi renovata, ut 
sciamus loca eorum, et altitudines, et magnitudines, et figuras, 
et multa quae oportet considerare in his. £t haec omnia 
fiunt per instrumenta ad haec idonea, et per tabulas, et per 
canoneSi id est, regulas ad haec certificanda inventas, quatenus 



iio OPERIS MAJORIS PARS QUARTA. 

via paretur ad judicia, quae fieri possunt secundum potes- 
tatem philosophiae, non solum in naturalibus, sed in his quae 
sumunt inclinationem ex natura, et gratis sequuntur coelestem 
dispositionem ; et non solum ad judicia praesentium praete- 
ritorum et futurorum, sed ad opera miranda, ut omnia pros- 
pera hujus mundi promoveantur, et adversa reprimantur, 
utih'ter ac magnifice. Nec sunt haec dubia. Nam patriarchae 
et prophetae a principio mundi certificaverunt haec, sicut 
caetcra. Et Aristoteles renovavit certificationem antiquorum, 
et produxit in lucem. Et omnes sapientes in rebus mag^is 
in hoc concordant, et experientia docet. Sed de his expositio 
fiet suo loco. 
Terrestrial Planum ergo est, quod coelestia sciuntur per mathematicam, 
go^vOTicd^ et quod praeparatur per eam via ad haec inferiora. Quod 
bycelestUl. autem haec inferiora non possunt cognosci sine mathematica, 
patet primo per hoc, quod non scimus res nisi per causas, 
si proprie accipiatur scientia, sicut Aristoteles dicit Sed 
coelestia sunt causae inferiorum. Ergo non scientur haec 
inferiora, nisi sciantur coelestia, et illa sine mathematica sciri 
non possunt. Ei^o horum inferiorum scientia dependet ex 
Thelaws eadem. Secundo possumus videre ex propriis, quod nihii 
offorcein horum inferiorum nec superiorum sciri potest sine mathe- 
vealedby maticae potestate. r^lam omnis res naturalis producitur m 
matic" ^^^^ P^^ efficiens et materiam in quam operatur, nam haec 
duo concurrunt primo. Agens enim per suamvirtutem movet 
et transmutat materiam, ut fiat res. Sed virtus efficientis et 
materiae sciri non potest sine magna mathematicae potestate, 
sicut nec ipsi effectus producti. Sunt ergo haec tria, efficiens, 
materia et eilectus. Et in coelestibus fit mutua influentia 
virtutum, ut lucis et aliarum, et est in eis alteratio, licet non 
ad corruptioncm. Et sic potest ostendi, quod nihil in rebus 
sciri potest sine geometriae potestate. Habemus ex hoc 
argumento, quod similiter aliae partes mathematicae sunt 
necessariae: qua ratione enim illa, et aliae: et proculdubio 
longe magis, quia nobiliores sunt. Si ergo propositum osten- 
datur in geometricis, non est necesse in hac persuasione de 
aliis fieri sermonem. 

Primo ergo ostendo propositum geometricae a parte 



MATHEMATICAE IN PHYSICIS UTILITAS. iii 

efficientis. LOmne enim efficiens agit per suam virtutem quam What is 
facit in materiam subjectam, ut lux solis facit suam virtutem ^^^. ^ 
in aere, quae est lumen diffusum per totum mundum a luce 
solari. Et haec virtus vocatur similitudo, et imago, et species * 
et multis nominibuSy et hanc facit tam substantia quam 
accidens, et tam spiritualis quam corporalis. £t substantia 
plus quam accidens, et spiritualis plus quam corporah's. u.£t 
haec species facit omnem operationem hujus mundi ; nam 
operatur in sensum, in intellectum, et in totam mundi mate- 
riam pep rerum generationejEyf, quia unum et idem fit ab 
agente naturali in quodcunque operetur^ quia non habet 
deliberationem ; et ideo quicquid ei occurrat facit idem. Sed 
si in sensum et intellectum agat, fit species, ut omnes sciunt. 
Ergo in contrarium, et in materiam fit species. Et in his 
quae habent rationem et intellectum, licet multa faciant 
secundum deliberationem et electionem voluntatis, tamen 
haec operatio, quae est generatio speciei, est naturalis in eis 
sicut in aliis. Unde substantia animae multiplicat suam 
virtutem in corpore et extra corpus, et quodlibet corpus 
extra se facit suam virtutem, et angeli movent mundum per 
hujusmodi virtutes. Sed Deus facit virtutes de nihilo, quas 
multiplicat in rebus ; agentia creata non sic^ sed alio modo de 
quo non est ad praesens curandum. Hujusmodi ergo virtutes 
agentium in hoc mundo faciunt omnem operationem. Sed 
duo sunt modo attendenda circa ista : unum est ipsa multi- 
plicatio speciei et virtutis a loco suae generationis ; et aliud 
est operatio varia in hoc mundo propter rerum generationem 
et comiptionem. Secundum sciri non potest sine primo. Et 
ideo oportet primo ipsam multiplicatiooem describi. 



Capitulum II. 

In quo canones multiplicationis virtutum agentium se- 
cundum lineas et angulos explicantur. 

' All Uiat is said in this fourth part of the Opus Majus on the subject of 
sptcUs must be studied in connexion with the much fuller treatment of the 
subject in the treatise De MuUipikations SpecUrum. 



112 OPERIS MAJORIS PARS QUARTA. 

Foroein Omnis autem multiplicatio vel est secundum Uneas, vel 

geneol» angulos, vel figuras. Dum vero species in medio raritatis 

rnedium unius incedit, ut in toto coelo, et in toto igne, et in toto aere, 

m^^ht vei in tota aqua, semper tenet vias rectas, quia Aristoteles 

lines. dicit quinto Metaphysicae quod natura operatur breviori modo 

quo potest, et linea recta est omnium brevissima. Quod etiam 

patet per vicesimum primi elementorum Euclidis dicentis, 

in omni triangulo duo latera sunt tertio longiora. 

The law of Sed cum corpus secundum est alterius raritatis et densitatis, 

refraction. j^ ^^ ^^^ ^jj. Qn^j^jjjQ densum, sed permutat aliquo modo 

transitum spedei, sicut aqua, quae est quodam modo rara, et 
quodam modo densa^ et crystallus similiter et vitrum, et hujus- 
modi per quorum media possumus videre, tunc species aut 
venit perpendiculariter super corpus secundum, et adhuc 
incedit per lineam rectam sicut prius ; aut si non cadat per- 
pendiculariter, tunc de necessitate mutat incessum rectum, et 
facit angulum in introitu corporis secundi. £t hujus de- 
cHnatio ab incessu recto vocatur fractio radii et speciei ^. Et 
haec causa est, quia perpendicularis fortior est et brevior, et 
ideo natura operatur meliori modo super eam, sicut docent 
geometricae demonstrationes, de quibus postea fiet mentio 
magis suo loco. Sed haec fractio est duplex, quoniam si 
corpus secundum est densius, prout accidit descendendo a 
coelo in haec inferiora, tunc omnes virtutes stellarum quae 
non cadunt perpendiculariter super globum elementorum, 
franguntur inter incessum rectum et perpendicularem du- 
cendam a loco fractionis. Et si corpus secundum est sub- 
tilius sicut est ascendendo ab aqua superius, tunc inter 
fractionem et perpendicularem ducendam a loco fractionis 

^ RefractioD is described for the first time In the optical work of Ptoiemy, 
the Greek text of which is lost, but of which an Arabic version was translated 
into Latin in the twelfth centuiy by the admiral Eugenio, who served under 
Roger, king of Sicily. This translation has been recently edited (1885) by 
Gilberto Govi of Turin. The account of refraction wiil be found in the.fifUi 
section of the work (p. 142 et seq.\ Ptolemy did more than state the fact of 
refraction. He measured the amount of deviation of the refracted ray for 
different angles of incidence, in the three media of air, water, and glass. As he 
shows himself to be aware of the error caused by refraction in astronomical 
observations (p. 151), it is strange that no mention of it should have been made 
in the Almagest, 



MATHEMATICAE IN PHYSICIS UTILITAS. 113 

cadit incessus rectus. Et haec est admiranda varietas in 
operatione naturae, sed nec mirum, cum infinita mirabilia 
fiunt per naturam secundum leges istarum fractionum; et 
per artificium juvans naturam possunt fieri ea quae mundus 
capere non potest, ut in scientia perspectiva explicabo. Sed 
cogetur per haec temporibus Antichristi ad ea quae ipse volet 
pro magna parte. 

Quod autem haec sint vera auctores docent, et omnes periti Artifidai 
sciunt, atque instrumenta possunt ad haec fieri, ut sensibiliter gence of 
hujusmodi incessus videamus ; sed usquequo habeamus instru- ^^)^- 
menta, possumus per efTectum naturalem hoc probare sine 
contradictione, ut docet haec figura. Accipiatur ergo dimidia 
sphaera crystalli vel vas vitreum, cujus inferius sit rotundum, 
plenum aqua. Cum ergo a centro solis veniunt radii per 
aerem ad corpus crystalli, vel vitri, 
quod est densius aere, illi qui non sunt 
perpendiculares super corpus tale (et hi 
sunt qui non vadunt in centrum ejus, 
ut ex geometricis -planum est), fran- 
guntur inter incessum rectum et per- 
pendicularem ducendam a loco frac- 
tionis, ut est radius ac^ qui cum 
transiverit per totum corpus vasis, 
venit ad aerem subtiliorem et non 
perpendiculariter. Ergo oportet ut sic 
vadat, ut incessus rectus sit inter ipsum 
et perpendicularem ducendam a loco 
fractionis, et ideo non ibit in ^, sed de- 
clinat ad/, super principalem perpendi- 
cularem, quae venit a stiie, ut est Of 
radius. Et eodem modo est ex alia 
parte, quod per duplicem fractionem 
A/concurret in eodem puncto/, in quo 
radius O f. Sed infiniti radii exeunt 

a sole super hoc corpus; ergo infiniti congregabuntur in eodem 
puncto per duph'cem fractionem. Sed congregatio luminum 
est causa caloris. Ergo ibi fiet calor comburens. Et hoc est 
verum, ut patet ad sensum ; nam si apponatur combustibile, 

VOL. I. I 




FlG. I. 



rcflcction. 



114 OPERIS MAJORIS PARS QUARTA. 

ut lana, vel bombyx, vel pannus, comburetur. Cum ergo hic 
sit combustio, et hoc fieri non potest nisi per congr^ationem 
radiorum, et radii non possunt congregari nisi per duplicem 
fractionem, quia una non sufficeret, nec tertia requiritur, ergo 
oportet ponere hanc varietatem fractionem, quod est mirabile 
In oculis sapientum. Nam unde est, quod natura sic operatur? 
Certe nihil est jucundum naturae, vel voluntati, nisi quod 
reficit varietas ; sed causae occultae sunt. Nec oportet causas 
modo investigare, cum per experientiam certissimam istud 
miraculum sciamus, et in sequentibus aliae experientiae sub- 
jungentur. 
Law of Quando vero secundum corpus est ita densum, quod nullo 

modo permittet transitum speciei, dico de sensibih' transitu, 
quantum ad judicium visus humani, tunc dicimus speciem 
reflecti. Secundum tamen Aristotelem et Boetium visus 
lyncts penetrat parietes. Ergo species transit secundum 
veritatcm ^, et hoc est verum : sed visus hominis non judicat 
dc hoc, sed de reflexione, quae necessario fit. Nam propter 

difficultatem transitus per den- 

sum, cum in aere a quo venit 

inveniat viam facilem, multiplicat 

se copiosius in partem a qua 

ventt. Et potest esse primo in 

generali duobus modis ; nam aut 

cadit perpendiculariter super 

FiG 3^ densum, et tunc redit in se 

omnino per eandcm viam a qua 

venit, et geminatur radius in eodem loco, Mt a b radius cadit 

perpendiculariter, et hoc est in planis ad angulos rectos, ut 

docetur in undecimo geometriae, sfcut in sphaericis, quando 

cadit in centrum. Et causa hujus est ; quia anguli incidentiae 

et reflexionis semper sunt aequales, ut multiplex demonstratio 

docet, et auctores omnes supponunt, et instrumenta ad hoc facta 

edocent ad oculum. Sed non sunt nisi duo anguli recti ex 

' Recent discoveries give much interest to this expression. Here, as in the 
case afterwards to be noticed of the time occupied in the passage of light, Bacon 
conceived that processes might take place of which human sense was not keen 
enough to take cognizance. See Dt MuU. SpecurMm, Pars II, cap. 5. 




MATHEMATICAE IN PHYSICIS UTILITAS. 115 

casu a b 2iA densum. Ergo per eosdem redibit radius reflexus, 
et ideo in ecdem loco. Sed linea a c quae cadit ad obliquos 
angulos, et non perpendiculariter, non redit in se ipsam, sed 
usque ad d, propter aequalitatem angulorum incidentiae et 
reflexionis. Quandocunque vero cadit radius ad angulos obli- 
quos, tunc angulus acutus vocatur angulus incidentiae ; et ab 
illo obtuso angulo separatur per lineam reflexam angulus 
aequalis angulo incidentiae, qui angulus continetur inter lineam 
reflexam et densum, ut est angulus d cg.et hic vocatur angulus 
reflexionis, quem oportet necessario aequari angulo acuto a 
parte altera, et hoc ad visum probamus in speculis. Nam 
non possumus videre res, nisi oculus sit in termino reflexionis, 
ut si oculus sit in dy videbit ; et si non. non videbit per illum 
radium reflexum. Et haec liota sunt, atque experientiae satis 
dabuntur de hoc in sequentibus. 

Possunt autem congregari radii infiniti per reflexionem, Artificial 
sicut per multiplicationem, ut fiant combustiones validae. g^^of 
Sed a plana superficie non possunt radii congregari in unum. reflectcd 
quia unus vadit ad unum locum, et alius ad .alium. Nec 
a convexo speculo ; sed a concavo sphaerico, columnari, et 
pyramidali,^annulari, «t ovali, et sic de aliis. Si ergo specu- 
lum concavum sphaericum ad solem ponatur, concurrunt radii 
infiniti in punctum unum per reflexionem. Et ideo oportet, 
ut speculo concavo ad solem posito ignis accendatur, sicut 
diciturultimo proposito Iibridespeculis,et ibidemdemonstratur. 
Sed instrumentum ad hoc factum esset pulchrum valde, et 
tunc videretur ad oculum, sicut prius dictum est de fractione. 
Unde si fieret speculum de chalybe bono, vel de argento, 
faciiius accideret combustio; sed una combustio non fit per 
omnes radios cadentes in speculo, sed per solos illos qui 
cadunt in circumferentiam unius circuli circa axem speculi, 
quia omnes, qui cadunt in una circumferentia, cadunt ad 
angulos aequales, et ideo reflectuntur ad punctum unum in 
axe, quia anguli reflexionum sunt aequales, et qui cadunt in 
alia circulatione, redeunt ad aliud punctum, et qui in tertia ad 
tertium, et sic de infinitis circulis imaginandis circa axem 
speculi: oportet enim quod ad puncta diversa vadant radii 
cadentes in diversis circumferentiis, propter hoc quod non 

I % 



ii6 OPERIS MAJORIS PARS QUARTA, 

cadunt ad angulos aequales. Et illi qui cadunt in minori 
circulo altius reflectuntur, et qui in maximo ad punctum 
infimum, scilicet ad polum sphaerae, seu ad extremitatem axis, 
reflectuntur. Sed nec natura nec ars contentae sunt hujus- 
modi combustione, imo volunt sic figurare corpora, ut omnes 
radii cadentes in totam superficiem speculi concurrant in 
punctum unum. Et sic adhuc ut in omni distantia quam 
volumus; et hoc est ultimum quod geometriae valet facere 
potestas. Nam hoc speculum potenter combureret omne quod 
posset objici. Et credendum est quod Antichristus his utetur, 
ut civitates et castra et exercitus comburat Quoniam si 
modica congregatio radiorum per fractionem vel speculum 
concavum comburit sensibiliter, quanto ergo magis in infini- 
tum, quando radii infinities infiniti congregabuntur per hoc 
speculum? Aestimant sapientes hoc esse necessarium. Et 
auctor in libro de speculis comburentibus docet hoc instru- 
mentum fieri, sed gratis in illo libro occultavit multum de 
artificio, et dicit quod in alio libro posuit residuum, quod non 
est translatum apud Latinos. Sed sunt Latini qui, mala 
gratia iilius auctoris occultantis perfectionem suae sapientiae, 
devenerunt ad hoc magnificum naturae secretum, quia ille 
auctor multum excitat peritos in sapientia ut residuum per- 
ficiant, et docet quod debet esse quasi annularis figurae, vel 
ovalis, ut, si amputarentur coni unius ovi, fieret annularis 
figura, si vero unus conus remanet, fit ovalis. Tali vero figura 
artificialiter facta secundum quod competit, oportet quod 
omnes radii cadentes in totam superficiem speculi cadant ad 
angulos aequales, et ideo reflectantur ad consimiles, et propter 
hoc in punctum unum. Elaboratur autem circa hoc speculum 
faciendum a peritissimo Latinorum ^, et Vestrae Magnificentiae 
gloria poterit praecipere, ut compleatur, cuni vobis fuerit 
annotatus. Haec autem triplex multiplicatio secundum lineas 

* This was Peter Peregrinus of Maricourt. See O^s Tertium, cap. 13. 
Reference to De MuU. Specierum (Pars II, cap. 7) will show that Bacon 
was aware of the properties of a surface produced by the rotation on its axis 
of a conic section. Vitello, Bacon's contemporary,* in the ninth book of his 
OpHcs, after proving geometrically that parallel rays falling on a parabolic 
mirror are reflected to the same point, expiains how such mirrors are constructed 
(lib. ix. prop. 44). 



MATHEMATICAE IN PHYSICIS UTILITAS. 117 

dicitur esse principalis propter hoc, quod ab ipso agente 
venit. 

Sed quarta est magis mundo necessaria, quamvis vocetur Diffused 
accidentalis multiplicatio. Nam lumen accidentale vocatur**^ 
respectu lucis principalis vententis a re, quoniam hoc non 
venit ab agente, sed a multiplicationibus principalibus, ut in 
domo cadit per fenestram multiplicatio principalis a sole, sed 
in angulo domus venit a radio fenestrae lux accidentalis. Non 
possent autem corpora mortalium semper exponi speciebus 
principalibus sine sui corruptione, et ideo temperavit Deus 
omnia per hujusmodi species accidentales. 

Quinta vero est aliena ab istis, nam non tenet l^es com- Propaga- 
munes naturae, sed sibi vindicat privilegium speciale. Et haec |hro^h*^^ 
multiplicatio non fit nisi in medio animato, ut in nervis sen- neives. 
suum : nam species sequitur tortuositatem nervi, et non curat 
de incessu recto, et hoc fit per virtutem animae regulantis in- 
cessum speciei, secundum quod opera rei animatae requirunt. 
De hac in perspectivis veritatibus aliquid dicetur. Quatuor 
primae sunt communes rebus mundi inanimatis, secundum 
quas natura delectatur operari; quinta ad sensum noscitur 
pertinere. 



Capitulum III. 
In quo datur multiplicatio secundum figuras. 

Deinde considerandum est, quo modo fiat multiplicatio From the 
secundum figuras. Et oportet quod multiplicatio fiat sphaerice. S^Jeds in 
Nam agens multiplicat se aequabiliter in omnem partem, et se- eycry 
cundum omnes diametros, et omnes difierentias positionis, quae 
sunt sursum, deorsum, ante, retro, dextrorsum, sinistrorsum. 
Ergo undique exeunt lineac in omnem partem ab agente 
tanquam a centro ; sed lineae undique exeuntes ab uno loco 
non possunt terminari, nisi ad superficiem concavam sphaerae. 
Et hoc patet, quia oculus non videt nisi per speciem venientem, 
sed si infiniti oculi ponerentur undique, omnes viderent eandem 
rem ; ergo per infinitas lineas exit species : sed infinitae non 
terminantur nisi ad superficiem sphaericam. Si vero dicatur, 



ii8 OPERIS MAJORIS PARS QUARTA, 

quod lumen intrans per magnum foramen triangulare vel 
alterius polygoniae figurae, non cadit sphaerice, sed quando 
intrat per parvum foramen ; dicendum est, quod latera parvi 
foraminis parum distant, et ideo lux in parva distantia potest 
figuram suam recuperare, sed quando transit per figuram 
magnam, non potest ita de facili, sed in aliqua distantia 
sufficienti, si obstacula amoverentur. Quod patet per xiv et 
XV primi elementorum Euclidis, ut ostendit figura. 




FiG. 3. 

Nam trahantur radii ab intersectione quantum est ab inter- 
sectione ad solem, oportet per dictas propositiones ut bases 
triangulorum sint aequales. Sed illae bases sunt diametri 
luminum. Ergo oportet ad minus, ut diameter speciei sit 
aequalis diametro solis in aliqua distantia, et per consequens 
multiplicatio erit sphaerica aequalis, et potest variari secundum 
diversitatem distantiae, sed semper sphaerice. Nec est 
instantia de luce ignis, quae ascendit in figura pyramidali: 
quia haec non est multiplicatio ex propria natura lucis, sed 
est propter motum corporis ipsius ignis, cujus accidens est 
lux, et accidens fertur secundum motum sui subjecti, sicut 
lux solis in sole. Pyramidaliter vero ignem necesse est 
ascendere, quoniam partes interiores semper elongantur a 
frigido circumstanti, et ideo minus impediuntur et citius 
expediunt se quam exteriores, et propter hoc altius ascendunt, 
et caeterae quanto iis propinquiores, tanto citius sese expediunt, 
et applicant se interioribus, aliquantulum deficientes ab 
intimarum altitudine, et sic gradatim per ordinem remotiores 
minus exaltantur, quia magis impediuntur a contrario circum- 
stanti ; et ideo oportet quod pyramis enascatur. Sed in 
sphaera possunt omnes figurae regulares inscribi, ut patet ex 
xiii libro elementorum Euclidis, inter quas una est pyramis. 

Et licet jam secundum rationem inscriptionis geometricac 



MATHEMATICAE IN PHYSICIS UTILITAS. 119 



Patiens 



non possunt figurae irregulares inscribi, nec figurae rotundae ; Cones of 

possunt tamen omnes figurae protrahi, et signari in sphaera. ^^^^^^ 

Et ideo non solum in sphaerica multiplicatione inveniemus each point 

pyramides lateratas, quarum proprium est inscribi in sphaera, surface 

sed pyramides rotundas ^, quae signari possunt et figurari in ^^^ <^"- 

sphaerica multiplicatione. Et haec 

cst figura, quam speciah'ter clegit 

natura in omni multiplicatione et 

actione, et non quamcunque pyra- 

midem, sed illam cujus basis est 

superficies agentis, et cujus conus 

cadit in ah'quod punctum patientis, 

quia sic potest a tota superficie 

agentis species venire ad singula 

puncta patientis per singulas pyra- 

mides et infinitas, ut patet in figura. 

Nan\ a quolibet puncto patientis fiunt 

radii infiniti, et ideo possunt com- 

binari infinities, ut fiant pyramides 

rotundac infinitae, quarum omnium est una basis, scilicet, 

supcrficies totius agentis ; et ad quamlibet partem patientis 

venit unus conus unius pyramidis, ut virtus veniat a toto 

agente ad quodHbet punctum patientis, et non ab aliqua parte 

determinata, quatenus virtus completa perveniat et tota, 

non partialis et imperfecta, ut fiat actio completa, quia natura 

facit secundum quod melius est. 




DISTINCTIO TERTIA. 

In qua declaratur varietas actionis naturalis per geometriam, 
habens tria capita. 



Capitulum I. 

His consideratis circa multiplicationem, sunt aliqua con- Indircct 
sideranda circa actionem ulteriorem. Nam lux per viam ^^^^ ^ 

* This is Bacon's expression for a cone. He uscs thc word conus to denote 
the apex of the cone. 



I20 



OPERIS MAJORIS PARS QUARTA. 



potent 
whcn 
directed 
vertically, 



multiplicationis suae facit speciem luminosam, et haec actio 
dicitur univoca, quia effectus est univocus, et unigenius, et 
conformis agenti. Sed alia est multiplicatio aequivoca, ut 
lux generat calorem, calor putrefactionem, putrefactio mortem, 
et vinum inebriat, et sic de omni agente, quod multos effectus 
facit praeter speciem suam et virtutem sibi univocam. Et sic 
sol et stellae faciunt omnia hic inferius, et angeli movent 
coelum et stellas, et anima corpus suum : virtus tamen agentis 
facit omnia ista, et haec est completa actio agentis et suae 
virtutis, ac a natura finaliter desiderata. De hac ergo actione 
considerandi sunt aliqui canones seu regulae, et propter eam 
principaliter, et tamen locum habent in actione univoca, et 
veritatem habent ibi. 
Force most Natura ergo, ut dictum est, fortius operatur super lineam 
rectam quam super curvam, quia brevior est, et minus facit 
patiens distare ab agente, et ideo plus capit de virtute 
ipsius sicut prope ignem aliquis plus calefit quam remotior. 
Caeterum melius est aequale quam inaequale^ ut dicit Boetius 
in practica geometriae. Sed in linea recta est aequalitas. 
Item omnis virtus unita est fortioris operationis, sicut dicitur 
in libro de causis. Sed uniformitas et unitas 
major est in linea recta, sicut dicit Aristoteles 
quinto Metaphysicae. Nam in curva est 
angulus, qui facit dispersionem et difformi- 
tatem, et repugnat unitati. Quapropter natura 
operatur fortius super h'neam rectam, quam 
super fractam vel reflexam. Sed linea recta, 
quae cadit ad angulos aequales, et perpen- 
diculariter, sive in planis, sive in sphaericis, 
illa est super quam natura eligit operari tum 
propter aequalitatem et majorem uniformi- 
tatem, tum propter brevitatem. Nam per xix 
propositum primi elementorum Euclidis, in omni triangulo 
majori angulo majus latus opponitur. Sed ex xvii primi 
ejusdem libri, major angulus in triangulo est rectus, scilicet, 
a c b. Ergo ei opponitur maximum latus scilicet, a b. 
Sed illa cadit non pcrpendiculariter. Ergo perpendicularis 
b c est brevior : quarc virtus veniens super eam operabitur 




FiG. 5. 



MATHEMATICAE IN PHYSICIS UTILITAS. 121 

fortius. Perpendicularis autem fortitudo non solum patet per 
demonstrationem, sed per experientiam, unde lapis cadens 
ab alto perpendiculariter fortius scindit ; et si homo cadit ab 
alto magis laeditur : nam qui hominem cadentem ab alto 
pelleret ab incessu perpendiculari, dummodo esset prope 
terram, non laederetur; quod si non fieret, moritur ex casu 
perpendiculari, et totus conquassatur. 

£t considerandum, quod si a diversis punctis agentis 
veniant ad eandem rem radii, unus perpendicularis super 
agens. et alius non perpendicularis super ipsum, semper erit 
perpendicularis brevior. Ut posito, quod agens sit a c, tunc 
a b est brevior quam c b^ 
et ideo fortior quantum est 
ex ratione hac. Et licet 
c b cadet super e d patiens 
ad angulos rectos, et ^ ^ 
non, ut sic c b fortificetur 
ex hujusmodi causa, nihiio- 
minus non attinget ad forti- 
tudinem a b^ quia brevior 
est, et quia b punctus e d 
similiter punctus est alterius lineae ut f g^ ad quam a b est 
perpendicularis, et sic b habet rationem patientis princi- 
paliter^ Et maxime super corpus sphaericum fit actio com- 
pletissima, cum virtus non cadat ibi ad aliquem anguium, 
sed transeat superficiem et corpus sphaericum, et nulla est 
diversitas vel diflformitas et plenitudo actionis ibi invenitur. 
Nisi enim signentur circuli in sphaera non est ibi angulus ; 
sed cum signantur ttmc anguli lineae perpendicularis erunt 
aequales, sicut in planis, et compiebitur actio. Sed tamen non 
sunt recti sed obtusi ut patet geometrae. 

Deinde sciendum est, quod natura operatur super h'neas Rcfracicd 
fractas fortius, quam super reflexas, quia fractio est in partem 511^.™^ 
incessus recti, sed reflexio in contrarium vadit, et contra than re- 

flccted 

incessum naturalem quem appetit natura virtutis incedentis in 
continuum et directum nisi impediatur, et ideo reflexio multum 
debilitat speciem et virtutem,et magis quam fractio. Sed hoc 

' Tbis sentence and the first part of the following are omitted in J. 




FiG. 6. 



zas OPERIS MAJORIS PARS QUARTA. 

intclligcndum cst de fractione et reflexione secundum pro- 
prietatem inccssus in eis. Si tamen consideremus, quod est 
rcflexio in eodem medio, et fractio in diversis, oportet quod 
duplcx medium magis impediat quam unum, et hoc saltem 
quando reflexio fit in medio subtili, et fiat fractio in secundo 
dcnsiori, ut cst in vase vitreo. Nam si congregentur radii 
a spcculo comburente, et post perspicuum comburens, oportet 
quod major sit combustio, sicut inferius suis locis cxplicabitur. 
Fractio vero quae est in corpore secundo densiori minus 
debilitat, quam ea quae est in corpore secundo subtiliori. Nam 
incessus perpendicularis est fortissimus, et idco quae magis 
accedit ad perpendicularem, magis est fortis. Sed fractio in 
corpore sccundo densiori declinat versus perpendicularem, quae 
ab codcm puncto cxit a quo fractio, ut patet superius in 
figura» tam in planis, quam in sphaericis, et ideo nulla minus 
dcbilitat De reflexione vero quae est ad anguios rectos, licet 
geminctur radius acddentaliter, et sic fit fortior actio, tamen 
de natura iilius reflexionis est, quod per se loquendo plus 
dcbilitat spcdem ; nam omnino est in contrarium conatus 
naturalis ipsius speciei, quoniam per eandem lineam redit 
spccics super quam venit. Sed quando est ad angulos 
obliquos, non est omnino in contrariam partem, sed a latere, 
ct ideo non tantum debilitat haec rcflexio^sicut alia. Quantum 
cst dc natura reflcxionis dico, scd propter geminationem 
virtutis in eodcm loco^ ct propter aequalitatem angulonim, 
ct conditiones perpendicularis, fortior est actio* 
i>i ixMi- £t tamen considerandum hic, quod j>er casum radiorum ad 

i«\^Vhc angulos obliquos possunt plures radii congregari per intersec- 
i:ix^itr tioncm, quam per radios cadentes ad angulos reclos, non solum 
«^Khqixs. cx pnopnctate speculorum, ut dictum est sed propter radios 
occurrentcs sibi infinities ex lcge inddentiae et rdlexicMiis ad 
angulos obliquos, skut acddit in aerey quando propter casum 
huju<;modi et retlexioDem tntersccant se ladii in quolibet 
puncto infinities. et fit calor. Xam paud sunt inddentes 
perpciKiiculariter super aliquam rem, quia non nisi ab imo 
puncto ax^entis cadit unus ptfpendicularis ad unum punctum 
paiicnt£s et ideo sxint paud neflexi Sed innniti noa perpen- 
ckulares exeuat a quolibet puacto agentis^ et iniuud rcAcxi 



MATHEMATICAE IN PHYSICIS UTILITAS. 123 

sunt eis respondentes. Deinde per casum perpendiculareni 
tantum duo conjunguntur in eodem loco aeris, scilicet, incidens 
et reflexus ejus compar. Sed per casum ad angulos obliquos 
incidentes inAniti se intersecant in quolibet puncto aeris. Et 
similiter incidentes penetrant reflexos non sibi compares, et 
reflexi reflexos infinities. Nam ad omne punctum terrae 
incidunt radii infiniti, et ab eodem infiniti reflectuntur, et ideo 
fortior operatio nascitur sic per accidens ex incidentibus et 
reflexis ad angulos obliquos, quam ad rectos. Ars vero potest 
juvare naturam in formatione actionis ; nam potest sic figurare 
specula, ut fiat congregatio virtutum magna per specula con- 
cava, et maxime per ovalia, sicut dictum est. Sed virtus 
principalis, sdlicet recta fracta et reflexa, est fortior acciden- 
tali, quia non venit accidentalis ab agente, sed a specie agentis, 
et est species speciei, propter quod debilior est. 



Capitulum II. 
In quo consideratur fortitudo actionis secundum figuras. 

Et cum pyramis, ut dictum est, requiratur ad actionem Short cones 
naturae, considerandum est quod conus brevioris pyramidis more^potent 
fortius operatur, tum quia minus distat ab ^^"* ^^^^- 

agente, tum quia radii conterminales circa 
conum pynimidis brevioris magis vicinantur, et 
vicinia radiorum ac congregatio fortius opera- 
tur; et hoc patet in figura. Nam per xvii 
primi elementorum Euclidis, omnes anguli 
circa punctum unum in superficie non vaient 
nisi quatuor rectos ; ergo quatuor anguli apud 
conum pyramidis brevioris valent reliquos 
quatuor apud conum longioris. Sed per xxi 
ejusdem, angulus in cono pyramidis brevioris 
est major quam angulus in cono pyramidis 
longioris, sdlicet a est major quam c ; et per ^10. 7. 

XV ejusdem, anguli contrapositi sunt aequales, 
scilicet a et *, item c et d\ ergo c eX d simul sumpti sunt 
minores quam a et * simul conjuncti ; ergo cum quatuor 




124 



OPERIS MAJORIS PARS QUARTA, 



simul sumpti aequantur aliis quatuor simul sumptis per xiii, 
tunc oportet quod A ctl sint majores quam / et e. Quapropter 
radii qui continent e magis vicinantur quam radii continentes A. 
Et eodem modo radii continentes / propinquiores sunt quam 
radii continentes /, et sic de infinitis radiis qui conterminales 
sunt in pyramide breviori, oportet quod omnes magis vicinentur 
quam radii qui simul terminantur in cono 
pyramidis longioris. Sed vicinia virtutum 
est causa fortioris actionis. Sed tamen cum 
incessus perpendicularium sit fortissimus, et 
omnis accessus ad perpendiculares fortior est 
recessu, tunc radii pyramidis longioris cum 
magis accedant ad perpendiculares a c b d^ 
erunt fortiores. Item tot radii veniunt ad 
conum pyramidis longioris, sicut ad conum 
brevioris, quoniam infiniti utrobique. Sed 
conus pyramidis longioris acutiorem habet 
Ergo radii ejus magis uniuntur. Ei^o 
Et dicendum est, quod hae rationes ad 




FiG. 8. 



angulum per xxi. 

fortius comburent. 

utramque partem demonstrationes sunt, sed fortiores sunt ad 

primam partem, et ideo praevalent. Unde quantum possunt 

rationes ultimae, tantum concludunt, sed aliae potentiores sunt 

et efficacius operantur. 



Mutual 
action of 
large and 
small 
spheres. 



Capitulum III. 

Quantum alteretur de patiente, et quantum de agente 
alterct, explanans. 

Ad haec subjui^ndum est quod in corporibus sphaerids 
aequalibus medietas cujuslibet recipit virtutem alterios, quia 
radii extremi contingunt corpora iila, et ideo transeunt per 
terminos diametri, et non attingit aliquis radius ad aliquam 
partem alterius medietatis. Sed corpus minus recepit virtutem 
majoris in majori sua portione, propter hoc quod radii extremi 
corporis majoris non aequidistant semper, sed concumint, et 
possunt ampiecti plus medietate minoris. Nam diameter cor- 
poris majoris est major diametro corporis minoris ; ct ideo 



MATHEMATICAE IN PHYSICIS UTILITAS. 125 



possunt radii exeuntes a terminis diametri corporis majoris 
transire ultra diametrum corporis minoris, ut majorem ejus 
portionem comprehendant ; et e contrario corporis majoris 






FlG. 9. 

minor portio recipit virtutem a minori corpore, quia diameter 
minoris corporis non aequatur diametro majoris, sed alicui 
chordae minoris portionis corporis majoris. Et nulius punctus 
sphaerici corporis potest facere virtutem a se, nisi ad spatium 
quod separatur ab eo per lineam quae contingat illud corpus 
in puncto ilio a quo fit virtus ; quoniam ab a puncto non 
potest aliqua linea cadere inter lineam contingentem et corpus 
sphaericum, ut demonstratur in 
XV tertii elementorum Euclidis. 
Et ideo spatium, quod est in 
angulo contingentiae, et sic per 
totam retro lineam contingentem 
versus corpus, non recipiet vir- 
tutem ab a puncto, sed totum 
spatium ultra lineam contin- 
gentiae, in quo sunt puncta^^rf^, 
recipiet virtutem. Et omnes 
radii qui cxeunt a supcrficie cor- 
poris sphaerici, quorum directio 

cadit in centrum corporis illius, sunt perpendiculares super 
ipsum et tales undique exeunt infiniti ut patet in figura. 
Et tum ab eodem puncto supernciei corporis, a quo fit 
radius perpendicularis, super idem corpus fiunt radii infiniti, 
ut patet ad a punctum, et sic de omnibus ; sed unus solus, 
scilicet a by radius est perpendicularis super illud corpus, 
quia ille solus, si protrahatur in continuum et directum, vadit 
in centrum corporis, et ideo ille est fortissimus, et habet longe 
plus de virtute. 




126 



OPERIS MAJORIS PARS QUARTA. 



Convergcnt 

rays from 

distant 

objects 

appear 

parallel. 



The central 
ray of each 
coneismost 
operative. 



£t isti radii perpendiculares, eo quod concurrunt in centrum 
corporis, non sunt aequidistantes ; potest tamen ocuius esse ita 
longe a corpore, quod non percipiat concursum, et judicabit 
radios tales esse aequidistantes, sicut accidit nobis de radiis 
solis et stellarum, et ideo judicamus umbras rerum diversarum 
aequidistantes, quando opponuntur soli, sed non secundum 
veritatem. Multa enim videntur aequidistare, quia non per- 
cipimus eorum concursum, ut parietes domus cujuslibet videntur 
ad sensum aequidistantes, sed non sunt quia omne grave tendit 
ad centrum naturaliter, et ideo rueret domus, si essent omnino 
aequidistantes. Et circuli meridiani diversarum civitatum 
videntur esse aequidistantes, et lineae meridiei, quia non per* 
cipimus concursum, et tamen concurrunt in polo mundi. 

Est etiam sciendum, quod radii qui cadunt in centnim 
corporis sphaerici a quo veniunt, sunt illi per quos judicamus 
stellas per foramina instrumentorum. Unde astronomus et 
perspectivus, qui experiuntur hujusmodi, utuntur istis radiis 
quia sensuales sunt et fortes. Quamvis enim a portione aliqua 
corporis sphaerici objecta rei patienti veniat una pyramis 
habens radios infinitos, qui fiunt a singulis punctis illius 
portionis, et omnes concurrunt in conum pyramidis cum radio 
perpendiculari, tamen unus solus est perpendicularis in una 
pyramide, et ille perpendicularis dominatur in fortitudine, et 
est axis pyramidis et tota pyramis ab eo nominatur apud 
experimentatores, et vocatur radius corporis agentis, ut patet 




FlG. II. 

in figura. Nam sit a centrum, ^t d c sit portio solis objecta 
terrae, et b conus pyramidis cadentis in terram, planum est 
quod e b radius cadit in centrum solis, et nulli alii qui sunt 
de corpore pyramidis, quamvis s'nt infiniti. Nam g b declinat 
a centro solis, ut patet, et sic de omnibus aliis/i, c b. Et ideo 



MATHEMATICAE IN PHYSICIS UTILITAS, 127 

est perpendicularis super corpus solis, et axis pyramidis, et 
ideo est fortior, et plus habet de virtute, quoniam virtus venit 
secundum hunc radium a tota profunditate solis, quod non 
accidit in aliis. Nam diameter h o est longior quam p q^ et 
quam omnes lineae cadentes in circulo a latere diametri, et 
ideo plus capit de substantia solis, ideo plus habet de virtute. 
YXh b linea est brevior quam c b^ et omnes aliae quae a por- 
tione soiis descendunt in terram, quapropter plus habet de 
virtute secundum praedicta. £t haec, quae nunc dicta sunt, 
patent ex viii tertii elementorum Euclidis. 



DISTINCTIO QUARTA. 
Capitulum I. 
In quo canones dicti applicantur ad lucem stellarum. 

His principiis et hujusmodi datis per vias geometriae, lllnstm- 
potest homo verificare omnem actionem naturae, quia omnis ^^^ 
veritas circa operationem agentis in medium, vel in materiam 
generabilem, vel in coelestia, et in totam mundi machinam, 
sumit ortum mediate vel immediate ex jam dictis, et quibus- 
dam similibus, quia non potui omnia in hac persuasione ponere, 
quae opus majus requirit. Et quod dico manifestare volo per 
aliqua exempla in diversis rebus mundi, et incipiam a supe- 
rioribus. Aristoteles vero dicit in primo Meteorologicorum * 
quod omnes steilae habent luccm a sole; et hoc patet perLunar 
eclipsin lunae : nam quando terra interponttur inter solem et ^ ^^^ 
lunam, ipsa' eclipsatur, et quando non, tunc illuminatur; et 
ideo similiter esset de aliis, si essent in tali situ in quo luna. 
Sed non sunt, nam conus pyraniidis umbrae non attingit nisi 
usque ad orbem Mercurii, ct ideo sola luna potest cadere in 
umbra tcrrae. Et tamen stellae inferiores eclipsant superiores, 
sicut Aristoteles vult secundo Coeli et Mundi,quando cadunt* 

Meteor, i. 8, % 6. Aristotle explains that thc earth's shadow reaches to 
the moon, but not much beyond ; and that the distance of the stars from the 
earth is many times as great as that of the sun ; wherefore, 6vayKri wivra r^v 
fkioy rii darpa mpiopdv, ical fitfBwl rifr y^f dyru^rrtiy airrwy, 

* In Meieor. i. 6, (11, Aristotle speaks of an occultation of one of the stars 
in Gemini by Jupiter. 



ia8 OPERIS MAJORIS PARS QUARTA. 

inferiores inter solem et superiores, et hoc bene accidit, sed 
non est ita notabile, sicut de luna. Sed quoniam, ut patet 
ex praedictis, rara et perspicua permittunt transitum speciei, 
ut aer et species oculi et stellarum transeunt per orbem ignis, 
et per medium omnium orbium septem planetarum, necesse 
est quod sint rara et perspicua, et quod non terminant visum. 
Ergo non sunt densa. Ergo nec visibilia, quia solum est 
visibile, ut docet Avicenna tertio de Anima, quod potest visum 
terminare, et verum est hoc. Sed si non sunt visibilia, non 
sunt lucida, quia lucidum est visibile. Et loquor de lucido 
quod habet lucem fixam, et non transeuntem ac propriam 
quae potest multiplicare a se radios, ut stella et ignis; non 
loquor de lucido quod recipit lucem transeuntem sicut aer, 
quem Aristoteles vocat lucidum ^ in secundo de Anima : sed 
hoc est aequivoce. Quapropter errant, qui aestimant sphaeram 
ignis lucere naturaliter, sicut hic inferius, et praecipue cum 
magts sit rarus quam aer^ et ideo minus visibilis, et propter 
hoc minus aptus luci, quia densitas est causa illuminationis, ut 
dicit Averroes secundo Coeli et M undi, et iibro de Substantia 
Orbis. Et similiter turpius erratur a vulgo, quando ponit 
orbes stellarum lucere, praecipue cum dicant quoddam falsum, 
et imponunt Averroi illud. Nam dicunt, quod stella non 
differt ab orbe nisi per majorem aggregationem et minorem 
lucis. Sed Averroes non dicit hoc, sed contrarium docet et 
probat : bene enim dicit totum hunc sermonem praeter casum 
genitivum ultimum, qui est /uciSy loco cujus dicit perspicui 
coelestis. Et quia fere omnia vocabula sermonis vulgati et 
ipsius Averrois sunt eadem, et aestimant perspicuum et luci- 
dum esse idem, propter verbum Aristotelis secundo de Anima, 
ubi accipitur lucidum aequivoce, imponunt Averroi quod velit 
orbem lucere propria luce et fixa, ut stella, licet minus. Sed 
dicit contrarium, volens quod propter fortitudinem actionis 
quam habet stella in hoc mundo, oportet quod multum 
habeat de substantia coeli congregata in suo corpore, et 
ideo perspicuum coeleste, quod dispergitur in partibus orbis^ 

* D€ Amma, ii. 7, $ a "Rrri S^ n dia^cs- &o^yh 3i Xiyca t ian fUv 6par6y, 
au an$' aM 8* 6par6r dAAd Ik' dXX^rpiw xp^/ta' towvtop 8' iarlv a^p «al v6»p . . . 
ipSn y ktrriv ^ rotrov lyipyfia rov Ikwpwovs f dia^or^s. 



MATHEMATICAE IN PHYSICIS UTILITAS. 129 

condensatur in corpore stellae, ut habeat fortem virtutem in 
alteratione mundi. Et ideo docet ibi, et in libro de substantia 
orbis, quod stella sola lucet, et nulla pars orbis. Et hic error 
vulgatur apud philosophantes, et apud omnes Theologos, 
quando ioquuntur, et scribunt de steliis. 

Quoniam vero in libro de proprietatibus elementorum isthe light 
dicitur, quod sol est sicut candela, et stellae sicut specula, ^^ s^rT" 
aestimat totum vulgus studentium quod lumen quod venit reilected 
ad nos de luna et stellis sit lux solis reflexa a superficiebuSguQ^ 
earum. Sed hoc cst impossibile propter aequalitatem angu- 
lorum incidentiae et reilexionis, ut patet in iigura. Nam ut 
prius visum est, si ita esset, tunc oportet angulum a incidentiae, 
et angulum b reflexionis aequari. Ergo b c radius non vadit 
nisi in partem determinatam 
terrae et non ubique, et sic de 
toto iumine quod venit ad su- 
perficiem lunae. Totum enim 
est quasi unus radius, et cadit 
ad angulos inaequales, et re- 
flectitur in partem determina- 
tam. Ergo si veniret ad terram, 
non illuminaret iuna nisi par- 
tem Horizontis aliquam deter- 
minatam ; sed nos videmus, 
quod illuminat totum hemi- 
sphaerium sicut sol. Ergo 
lux illa quae venit a luna et a ^'^* "' 

stellis non est reflexa. Et Averroes secundo coeli et mundi 
hac demonstratione utitur, et sua confirmat auctoritate, quod 
non est lumen solis reflexum a superficie stellarum, quod ad 
nos descendit ab eis, sed proprium lumen et innatum, eductum 
tamen de potentia materiae in corpore stellae per virtutem 
solis venientis ad stellam, quae virtus alterat et transmutat 
stellam, et facit lumen in ea ; et quando habet lumcn natu- 
raliter genitum in ea, sicut sol habet lucem creatam, tunc 
potest multiplicare lucem a se undique sicut sol. Et tunc 
concedendum est quod lumen solis reflectitur a superficie 
lunae, sed non venit ad terram, sed ad aliam partem mundi 

VOL. I. K 




130 OPERIS MAJORIS PARS QUARTA. 

decUnat in coelestibus secundum aequalitatem angulorum 
incidentiae et reflexionis. 
Morethan Et per supradicta patet, quantum illuminatur de terra et 
eaith^illu- ^^ stellis per solem. Nam majores earum portiones semper 
minated iHuminantur, quia minores sunt sole. Sol enim est centies 
' septuagies fere major tota terra, sicut ostendit Ptolemaeus in 
quinto Almagesti *, et sic possunt omnia quae pertinent ad illu- 
minationes et protractiones radiorum in coelestibus verificari, 
ut in diversa figuratione lunae secundum aetates, et quare in 
eclipsibus appareat rubea et pallida, et tota ratione eclipsis ; 
nam hoc est propter lumen principale, quod a radiis princi- 
palibus venit infra umbram, et quodammodo sic imperfecte 
illuminatur per radios accidentales. Et non solum de his, sed 
de aliis virtutibus factis a planetis et stellis in alias secundum 
omnes diversitates conjunctionum et aspectuum, quibus astro- 
nomi utuntur in suis considerationibus, in quibus multipli- 
cantur non solum radii lucis, sed virtutes substantiales stellarum 
ad invicem, secundum quod dicimus lunam in Ariete esse 
calidam et siccam, in Geminis calidam et bumidam, et in 
Cancro frigidam ct humidam : et quando conjungitur Saturno 
fit frigida et sicca, et quando lovi calida et humida, et sic de 
omnibus talibus. Nam haec omnia certificantur per multi- 
plicationes specierum et virtutum determinatas juxta principia 
praetacta. Et non solum haec, quae pertinent ad qualitates 
et naturas substantiales stellarum, sed ea quae pertinent ad 
figuras, et magnitudines, et altitudines, ct numerum coelonim 
et stellarum, ct ad hujusmodi consimilia. 



Capitulum II. 
In quo canones supradicti applicantur ad totum mundum. 

In si>ace Et non solum haec de coclestibus verificantur per dicta, 
^Ta^ihan ^ ^^ elemcntis et toto mundo. Nam cum philosophi ante 
one, as Aristotclcm posuenint omnia csse unum corpus mundi, potcst 
provis!'*" destnii hoc per lcges fractionis. Nam si quis per instnimenta 
quibus cxpcrimur ca quae sunt in coelestibus, cujusmodi 

» PloL Symimxis, i. i6t 



MATHEMATICAE IN PHYSICIS UTILITAS. 131 

vocantur armillae vel alia, accipiat locum alicujus stellae circa 
aequinoctialem in ortu suo, et deinde accipiat locum ejusdem 
quando venit ad lineam meridiei, distare sensibiliter inveniet 
eam in loco meridiei plus a polo mundi septentrionali, quam 
quando fuit in ortu. Ergo visus videt stellam diversis modis 
in illis diversis temporibus : nam si videret eodem modo tunc 
steliam in eodem ioco inveniret semper. Sed quando stella 
est in linea meridiei, tunc stella accedit ad zenith capitis 
aspicientis, qui est punctus in coeio suprapositus capiti, qua- 
propter cadunt radii in visum perpendiculariter, et in centrum 
mundi, et ideo non franguntur, et propter hoc videt visus 
stellam per rectas lineas in suo loco vero. Ergo quando visus 
errat in ortu stellae non videbit per lineas perpendiculares, 
quia multum distat stella a zenith capitis, et ideo radii cadunt 
ad angulos obliquos, quapropter franguntur, et ideo visus tunc 
videt per lineas fractas, et errat in loco stellae. Sic autem 
Ptolemaeus ^ in libro quinto de opticis docet considerare, et 
Alhazen in libro septimo et ego consideravi in instrumentis 
hoc idem, et certum est. Quoniam ergo fractio radiorum cadit 
in hoc mundo, planum est quod plura corpora sunt in mundo. 
Et prima fractio invenitur secundum considerationem dictam Ray pass- 
in superficie ignis immediate sub orbe coelesti, scilicet sub j^ar**™ 
sphaera lunae : quapropter sphaera ignis est diversa a sphaera sp^we to 
coeli ; cum tamen Platonici et Augustinus, et multi autores firc is 
antiqui tangant Platonice quod ignis et coelum sunt unius "^^™*^*^- 
naturae. Sed hoc est impossibile propter demonstrationem 
dictam, et propter alias demonstrationes naturales quas Ari- 
stoteles in libro Coeli et Mundi aflfert, quibus nullus modernus 
modo contradicit: nam trita est haec veritas in naturalibus. 
Haec tamen demonstratio vulgo naturalium est ignota, nam 
Aristoteles non tangit eam, nec ejus expositores. Quoniam 
autem non est fractio in sphaera aeris, ut iidem autores 
docent, et certitudo experientiae, ideo multum turbantur 
sapientes, an sphaera aeris et ignis sint duae vel una. Videtur 
enim per autores praedictos, et propter privationem fractionis, 
quod una sit superficies aeris et ignis, et unum corpus. Sed 
hoc est impossibile, quia Aristoteles dicit tertio Coeli et Mundi, 

^ Ptol. Opiica€y V. p. 151, ed. Govi. Cf. Alhazen, vii. 15. 
K % 



132 OPERIS MAJORIS PARS QUARTA. 

quod aer est gravis^ in sphaera sua, et sequitur naturaliter 
superficiem aquae non ignis ; nam si ignis ascenderet in 
sphaera sua, aer non sequeretur, ut dicit quia cum aqua 
descendit, aer sequitur ejus superficiem, ut videmus ad ocu- 
lum. Quapropter non erunt unum corpus aer et ignis ; et tota 
dubitatio solvitur per legem fractipnis. Nam tria requiruntur 
ad hoc ut sit fractio, scilicet ut corpus secundum habeat 
superficiem distinctam a primo, et quod sit aiterius raritatis, 
scilicet magis rarum vel minus, et quod radii cadant ad 
angulos obliquos. Quod si aliquid istorum deficiat, non est 
fractio possibilis. Propter primum enim non est fractio in 
eodem corpore, licet habeat partem unam rariorem et aliam 
minus raram, sicut aer est rarior superius quam inferius. Et 
propter secundum non est fractio in orbibus coelestibus, quia 
sunt ejusdem raritatis, quantum ad sensum nostrum. Et 
propter hoc idem non est fractio in sphaera aeris, quia aer 
gradatim subtiliatur usquequo in sua parte suprema aequetur 
subtilitati ignis in parte inferiori, et ideo non est ibi fractio. 
Quoniam autem fractio haec est inter incessum rectum et 
perpendicularem ducendam a loco fractionis, ut docent hi 
autores, et ipsa experientia, ideo sequitur quod corpus se- 
cundum est densius priori et ideo corpus sub orbe coelesti 
est densius quam orbis coeli. Quapropter oportet ponere 
plenam diversitatem corpDrum mundi penes coelum et ele- 
mentum. Et quando habuerimus haec, tunc per radios, et 
pyramides luminosas stellarum venientium ad instrumenta 
certificabimus omnia quae sunt in coelestibus, scilicet numerum 
coelorum, et stellarum magnitudinem et spissitudinem, et 
omnia quae sunt in coelis. 

Capitulum III. 

In quo per multipHcationes praedictas investigantur com- 
plexiones locorum mundi circa polos ejus. 

Laws of Posthaec descendemus ad sphaeras elementorum et investi- 
Polar gabimus omnes complexiones eorum secundum singulas partes 

* De CoelOy iv. 4, § 5 ^»' tJ airrov yi^ X^P? iravro iS<ipos Ix" *^^ »v/x>s, kcU 
6 a^p. 



MATHEMATICAE IN PHYSICIS UTILITAS. 133 

habitationis, et inveniemus quod loca sub polis mundi sunt tcmpera- 
naturaliter inhabitabilia propter frigus. Nec obstant nobis ^^^^^ ' 
rationes superius annotatae pro pyramidibus longioribus, nam standing 
sicut ibi dictum est, demonstrationes pro pyramidibus brevi- ^^\j^ ° 
oribus vincunt in hac parte, quamvis omnis homo qui nesciret summer. 
hujusmodi radices multiplicationis lucis vinceretur per pyra- 
mides longiores. Sed verum est, quod coni pyramidum 
venientium ad loca sub polis nimis distant a sole, et ideo 
debiles sunt, nec possunt nisi elevare vapores ab aqua et terra 
in aerem, et non possunt eos consumere ; et ideo oportet quod 
aer sit densus et caliginosus et congelatus per vapores ubique 
et semper, ut ibi plantae et animalia non possint vivere, sicut 
docet Ptolemaeus in libro de dispositione sphaerae. Sed si 
cum pyramidibus longioribus addamus autoritatem Aristotelis 
secundo de vegetabilibus dicentis, *quod apud eos^ ubi prolon- 
gantur dies/ &c. et hoc est, ut docet commentator super illud 
verbum, ubi est dimidius annus dies, et dimidius annus nox, 
non sunt animalia nec plantae, quia calor combussit materiam 
eorum; videbitur quod illa loca sub polis sint inhabitabilia 
propter calorem, non propter frigus. Nam proculdubio ibi est 
dimidius annus dies, et tunc videretur quod calor nimis abun- 
daret, dum sol ingreditur primum gradum Arietis, usquequo 
veniat ad primum gradum Librae, et hoc per dimidium annum. 
Et adhuc additur quod diluculum matutinum incipit per 
mensem et dimidium ante ortum solis super terram, et crepus- 
culum vespertinum durat per mensem et dimidium ultra 
occasum solis, ita ut lumen solis appareat super terram ante 
ortum et occasum per totum tempus dictum, sicut nobis in 
aestate post occasum et in aurora apparet lux solis; quare 
per longitudinem crepusculi et aurorae multum augmentabitur 
calor, quia non habent noctem profundam nisi per tres menses 
anni, ut certum est per omnes autores et singulos sapientes. 
Item sol nunquam recedit ab eis, nisi per maximam solis de- 
clinationem, quae fere est 24* gradus, quia aequinoctialis est 

• The rcference apparenily is to the apocryphal work, De PlanHs, lib. il 7 
'Ecb^ 6 likun luucp&niTa rp ^/li/if wpoc6yjf h rp icaHjoti ttirrov ital Moranfpitv^ r^ 
irfpirtjros obic Ix** '''^ fvrdy Svrdfif if fvXXa mt Kopwohs wpo&ftiw, 

* It may bc noted, once for all, that in Uie oldest MSS. of the Ofms MajuSy 



134 OPERIS MAJORIS PARS QUARTA. 

Horizon eorum. Sed a nobis recedit sol per duplicatam 
declinationem, scilicet fere per 48 gradus. Ergo ex hujusmodi 
appropinquatione augmentabitur calor. Quapropter con- 
cluditur secundum veritatem, quod loca sunt ibi inhabitabilia 
propter calorem. Sed cum Plinius in naturah'bus et Martianus 
in descriptione regionum mundi invenerunt per experientiam 
certam, quod regiones sub poh*s sunt temperatissimae in hoc 
mundo, sicut ipsi dicunt, et allegant experientiam hominum 
qui ibi fuerunt, non possumus n^;are quin ibi sint regiones 
temperatissimae ; et quis concordabit tantam contrarietatem ? 
Certe nullus, nisi optime sciat principia multiplicationis et 
actionis specierum. Persuasionem ergo do ad hoc, quod 
naturah*ter secundum dispositionem loci respectu coeh' et solis 
oportet quod locus sit inhabitabilis propter frigus; et sic 
currunt auctoritates permultae. 
Tempeia- Sed propter accidentalem dispositionem loci, simul cum 
fied ™^' aliquibus causis naturalibus, potest ibi aliqua regio esse 
mountain combusta, et aliqua temperata. Nam propter rationes de 
rangc^ longioribus pyramidibus, et propter longitudinem diei, et 
propter magnitudinem crepusculi et aurorae, et propter 
hoc, quod sol non recedit ab eis nisi per maximam solis 
declinationem, si adjungamus causam accidentalem cum 
his, forsan inveniemus quod quaerimus. Nam proculdubio, 
secundum quod Plinius et Martianus ^ et alii docent, montes 
maximi sunt ad ubera aquilonis, ut montes Riphaei et Hyper- 
borei et alii, quorum altitudo immensa est, propter quam 
possunt prohibere frigus aquilonis, sicut accidit in montibus 
Italiae apud loca quae sunt inter solem et montes. £t simul 
cum hoc additur, quod montes inveniuntur lapidei, et alii 
coagulati in crystallum et salem, sicut videmus in pluribus 
locis mundi, qui montes habent superficies magis politas et 
aequales, propter quod ab eis potest fieri major et melior 
reflexio quam a montibus asperis. Nam a superficie polita 

diose which are contemporary with Bacon, Arabic numerals are generally used ; 
invariably so where the numbers are large. 

^ For Pliny*s account of the enviable life of the Hyperboreans see Hist 
Naturetl. iv. la. Martianus Capella was a writer of the fiilh century. His 
work, much read in the Middle Ages, was a scientific encyclopaedia bearing the 
fanciful tiUe, J>t nupHis phihlogiae ei Menurn de sepient artibus iiberalibMS. 



MATHEMATICAE IN PHYSICIS UTILITAS. 135 

et aequali et leni fit sensibilis reflexio, ut patet in speculis : 
et hoc est, quia partes concordant in unam actionem, et non 
dissipatur species, sed integra redit sicut venit ; sed propter 
inaequalitatem superficiei corporis asperi nulla pars concordat 
cum alia, sed elevatior primo reflecfit, et depressior secun- 
dario, et sic tota species dissipatur nec venit integra, propter 
quod non videmus per corpora aspera sed polita. Bonitas 
ergo reflexionis, quae potest inveniri in locis aliquibus circa 
polos propter polituram superficierum montium, valet co- 
operari ad calorem generandum simul cum aititudine montium. 
Et ulterius considerandum est, quod montes habent varias 
flguras, nam aliquis potest habere figuram ad modum specu- 
lorum comburentium, et alius ad modum speculorum sphaeri- 
corum vel columnarium vel pyramidalium, et ubi flgura speculi 
comburentis invenietur cum caeteris causis caloris, necesse 
est ibi esse combustionem validam, ita ut nihil ibi vivere 
possit, et sic intelligendus est Aristoteles cum ejus commen- 
tatore. Ubi autem temperantur causae caloris et frigoris, et 
penes altitudinem montium, et penes lenitatem superflcierum, 
et penes figuram, necesse est quod sit locus temperatus, et 
sic intelligendi sunt Plinius et Martianus et caeteri experi- 
mentatores. 



Capitulum IV. 

In quo investigatur complexio locorum, qui sunt in medio 
mundi. 

Mundi vero loca in quibus sumus per totam habitationem CUmate of 
usque versus finem tertii climatis sunt tolerabilis caloris. JJJJ^*^*^^ 
Hierusalem quidem est in tertio climate, sed ultra sub Tropico tropicai 
Cancri incipit torrida zona, et locus malae habitationis. Et 
propter hoc, quod via solis est inter duos Tropicos, aestimat 
vulgus quod totus ille locus est combustus et quod nihil ibi 
sit temperatum ; et ideo aestimant, quod locus sub aequi- 
noctiali circulo sit maxime combustus, quia sol super capita 
habitantium bis transit in anno, et non attingit ad Tropica 
nisi semel, ut in solstitio aestivali venit ad Tropicum Cancri, 



136 OPERIS MAJORIS PARS QUARTA. 

et in solstitio hyemali accedit ad Tropicum Capricomi. Sed 
eundo de uno ad aliud transit bis super aequinoctialem 
circulum, scilicet in principio Arietis et Librae, et hoc est 
in principio veris et autumni, propter quod aestimatur 
a multis, quod locus sub aequinoctiali sit maxime com- 
bustus, et ad hoc faciunt rationes secundum multiplica- 
tiones praedictas. Nam ibi saltefti bis in anno sunt pyramides 
breviores et radii cadentes ad angulos rectos ac perpendi- 
culares, et per consequens non franguntur ; redeunt in se ut 
geminentur radii, et ideo videtur prima facie quod tota forti- 
tudo actionis naturalis ibi concurrit longe plus quam alibi. 
Sed constat nobis quod sub Tropicis sunt Aethiopes cona- 
busti. Ergo videtur quod locus sub aequinoctiali circulp 
sit combustissimus, sicut vulgus ponit. Sed proculdubio 
Ptolemaeus vult libro praedicto, quod locus ille sit temperatus 
respectu Tropicorum. Atque Avicenna docet primo de 
Animalibus, et primo artis medicinae, quod locus ille est 
temperatissimus. Et propter hoc theologi ponunt his diebus, 
quod ibi sit paradisus, et ideo vulgus indoctum errat in hpc 
loco. Et tenebimus sententiam Ptolemaei ad minus, quic- 
quid sit de opinione Avicennae et theologorum, quamvis leges 
multiplicationis specierum hic concludant quantum possunt. 
Scd causae fortiores sunt in contrarium, quas Avicenna 
egregie assignat, videlicet quod declinatio solis magna est ibi, 
et aequidistantes sunt distinctae et distant multum. Nam 
cum tota declinatio solis sit fere 24 gradus de Coluro, 
fere la debentur signis aequinoctialibus, scilicet Arieti et 
Virgini, Librae et Piscibus, et octo fere debentur Tauro, 
Leoni, Scorpioni, Aquario, et ut fere quatuor debentur 
Geminis, Cancro, Sagittario, Capricorno. Et ideo quando 
sol est in signis ubi declinatio est fere 4 graduum, fertur 
propter confusionem aequidistantium supcr eandem regionem 
per 40 dies, et comburit ut in Tropicis. Sed minus in aliis 
ubi declinatio est octo graduum, minime vero ubi est 12, 
et hoc est apud aequinoctialem. 
Effect of Alia causa est propter aequinoctium, quia aer tantum tempe- 
ccntricity. ^^^^^ ^^ nocte, ut non possit essc calor superfluus de die, et 
propter hoc ibi est aequalitas aeris, et nobiles complexionum 



ARiESl V Xr^^ . T LlBRA 



MATHEMATICAE IN PHYSICIS UTILITAS. 137 

dispositiones, ut docet Aviceona. Nec est dubium quin locus sit 
temperatus, sed an sit temperatissimus, non percipio adhuc. £t 
ideo non est certiiicatum an paradisus debeat ibi esse. Quoniam 
si eccentricitas solis sit prout mathematici ponunt, impos- 
sibile est pure tempcratum esse sub aequinoctiali. Nam una 
pars eccentrici, quae vocatur oppositum augis descendit ad 
terram per quinque partes semidiametri eccentrici magis quam 
reliqua quae dicitur aux^. Et ideo quando sol venit ad oppo- 
situm augis comburit terram omnino, ut nihil ibi vivere possit, 
tum propter appropinquationem, tum propter casum radiorum 
ad angulos rectos, tum propter confusionem aequidistantium 
in quibus moratur super eandem regionem ut comburat eam ; 
et hoc est quando sol est in 
Sagittario et Capricorno et 
Scorpione. Nam oppositum 
augis est in Sagittario, et in 
locis propinquis ei comburit 
similiter et distemperat £t 
ideo sol distemperabit Li- 
bram et Arietem. Nam jam 
transivit medietatem eccen- 
trici, quando venit ad initium 
Librae, et Libra satis appro- 
pinquavit ad oppositum augis, ut intemperiem caloris possit 
causare, sicut patet in figura. Sed constat, quod paradisus 
habet plenum temperamentum. Horum autem certificatio 
non est praesentis persuasionis. 



Capitulum V. 

£t ideo *^ redeo ad propositum dicens quod complexiones influence 
locorum mundi inveniri non possunt, nisi homo sciat leges ^^em*^^ 

* Aux is the Arabian form of the word apsis : used together with the rclated perament. 
expression oppositum augis to denote the two points of an orbit which are at the 
greatest or least distance from the centre of motion. In modem astronomy 

the aphelion or apogee of the earth^s or the moon's orbit would be called 
sumtna apsisy or aux ; the perihelion or perigee would be ima apsis, or opposi- 
tum augis. It need hardly be mentioned that in the Hipparchiau or Ptolemaic 
theory the 8un*s orbit was supposed to be eccentric to the circle of the heavens. 

* I foUow O. in making this the beginning of a new chapter. 




FlG. 13. 



138 OPERIS MAJORIS PARS QUARTA. 

multiplicationum praesignatas, quoniam nec falsum vitabit, 
nec verum poterit confirmare. Sed locus est principium 
generationis, quemadmodum et pater, ut dicit Porphyrius. 
Et nos videmus, quod omnta variantur secundum loca mundi 
diversa non solum in naturalibus, sed homines in moribus ; 
quoniam alios mores habent Aethiopes, alios Hispani, alios 
Romani, et alios Gallici. Nam et Picardi, qui sunt veris 
Gallicis vicini, habent tantam diversitatem in moribus et in 
Itngua ut non sine admiratione possit esse unde sit tanta 
diversitas locorum propinquorum. 

Sed quoniam res hujus mundi in diversis locis consti- 
tutae, quantumcunque propinquae sunt, recipiunt conos 
diversarum pyramidum venientium a toto coelo objecto eis, 
ideo accidit infinita diversitas. Nam ad singula puncta terrae 
veniunt coni pyramidum singularum, et quilibet punctus est 
centrum unius Horizontis novi. Et ideo videmus, quod 
duae herbae simul nascuntur de terra sine medio, et ideo 
duo gemelli in ventre matris sortiuntur diversitatem com- 
plexionis, ut postea mores habeant diversos, et sequantur 
artes diversas, et occupationes diffbrmes per totam vitam. 
Et ideo virtutes coelorum et stellarum producunt ubique 
diversas res in proprietatibus et naturis, et in rebus gene- 
ratis secundum propagationem. Et non solum multiplicatio 
virtutis coelestis operatur, sed patris et matris, quoniam 
descinduntur virtutes in seminibus, ut docent medici. Et 
praedpue ab anima matris continuatur multiplicatio virtutis 
et speciei super foetum usque in complementum generationis 
et nativitatis. Et cum puer in nativitate exponitur aeri novo 
tanquam alteri mundo, tunc recipit conos pyramidum coele- 
stium secundum singulas partes, et sic recipit impressiones 
novas, quas nunquam dimittit, quia quod nova testa capit, 
inveterata sapit Et tunc confirmatur complexio radicalis, 
quae semper manet usque ad finem vitae, licet complexio 
currens mutetur tota die. Et ad hanc radicalem complexionem 
sequuntur inclinationes ad mores et ad scientias et ad linguas, 
et ad quaecunque artificia et n<^otia, et ad omnem diversi- 
tatem quam videmus in omnibus. Et si coeli dispositio sit 
mala in conceptione et nativitate pueri, tunc coni pyramidum 



MATHEMATICAE IN PHYSICIS UTILITAS, 139 

laedunt complexionem, et per consequens inclinatur homo ad 
malos mores et artes perversas, secundum diversitatem coelestis 
constcllationis : et si constellatio bona est, tunc complexio est 
bona, et sequitur inclinatio ad mores bonos et scientias utiles : 
et si mediocritas accidat in coelesti constellatione^ tunc homo 
mediocris est in omntbus quantum est ex naturali dispositione, 
licet poterit se mutare per libertatem arbitrii, et per gratiam 
Dei, et per tentationem diaboli et per bonum aut malum 
consilium, maxime a juventute. Et nunc quae dixi in univer- 
sali, possunt confirmari si tempus esset per exempla in singulis 
rebus. Sed jam de combustione facta per crystallum et 
vitrum et specula concava et alia quae ad oculum patent, 
ostenditur nobis sensibiliter, quod fractiones et reflexiones et 
hujusmodi multiplicationes possunt effectus naturales produ- 
cere. Atque vulgatum est quod irides et cometae et plures 
aliae impressiones inflammatae in aere, et circuli circa solem 
et lunam, fiunt per hujusmodi multiplicationes radiorum, cum 
aliam causam non possunt habere. £t sic de omnibus aliis, 
licet non sit in singulis evidens, quia non omnium agentium 
species sunt visibiles. 



Capitulum VI. 
In quo datur causa fluxus et refluxus maris per radios. 

£t nunc ponam unum exemplum omnibus occultum, etThetides. 
pono ubi minus videtur quod multiplicatio secundum lineas 
et angulos determinatos requiratur, ut in re quam diflicillima, 
quae tamen per multiplicationem redditur satis plana ; et est 
de fluxu et refluxu maris. Alpetragius vero in libro suo de 
motibus coelestibus aestimat, omnia corpora mundi praeter 
terram moveri motu coeli primi, et hoc verum est: sed 
secundum quod magis elongantur tardius moventur, et cum 
majori impedimento. Unde aqua tardius et irregularius 
movetur in sphaera sua, quam alia corpora mundi. Addit 
ergo iste, quod hic motus facit fluxum et refluxum ; sed non 
placet hic, quia fluxus et refluxus sunt determinati et certi, et 



I40 OPERIS MAJORIS PARS QUARTA. 

currunt sicut luna variatur in partibus coeli. Sed motus aquae 
a motu coeli est confusus, et inordinatus, et irregularis propter 
hoc, quod virtus coeli primi nimis elongatur ab ejus origine, 
quando est in aqua, et ideo praevalet virtus aquae propria, 
scilicet sua gravitas, quia nititur quiescere in loco suo, propter 
quod non potest hic motus esse ita regularis et distinctus 
temporibus certis penes accessus et refluxus ut nos videmus 
in mari. Et ideo Albumazar in majori introductorio astro- 
nomiae determinat omnes differentias fluxus et refluxus, et 
narrat quod accidunt omni die et nocte secundum quod luna 
Flood tide est in diversis partibus sui circuli et respectu solis. Sed non 
u^^™^*^° dicit nobis causam, nisi quod luna est causa, et quod quando 
proaching luna est in uno loco tunc est fluxus, quando in alio tunc est 
refluxus. Propter quod considerandum est, quod quando 
luna ascendit super mare alicujus regionis, ejus radii cadunt 
ad angulos obliquos, ut quilibet qui novit casum angulorum 
potest hoc scire. Et quia cadunt ad angulos tales, oportet 
^quod sint debilis virtutis, ut prius ostensum est. £t ideo 
solum possunt elevare vapores a fundo maris, et ampullas 
tumentes, et ingurgitantes aquas maris, ut expellantur a canali- 
bus suis, quos vapores non possunt radii ad aerem extrahere 
nec consumere propter debilitatem suam ; et ideo oportet ut 
aqua fluat a sedibus suis, donec durat hujusmodi ebuUitio 
vaporum. Sed cum luna accedit ad medium coeli, cadunt 
magis et magis radii ejus ad angulos rectos, et fortiflcantur 
super corpus maris, ac extrahunt vapores ad aerem et con- 
sumunt, unde debiUtatur fluxus paulatim, secundum quod luna 
appropinquat lineae meridiei ; et quando venit ad illam lineam 
sunt vapores castigati et consumpti, ita ut statim dum luna 
descendit ad aliam quartam coeli incipiat refluxus^ quia ces- 
sante causa cessat effectus. Et pono exemplum sensibile ad 
istud. Nam in puimento posito super ignem, ignis in principio 
resolvit vapores, et facit eos exire orificium vasis: quando 
vero fortificatus est et continuatur consumit vapores, et liquor 
residet in fundo vasis. Nam universaliter calor debilis resolvit 
vapores et non consumit, calor enim solis fortis consumit, 
unde in nocte, et in mane, et in vespere fit resolutio vaporum 
major quam in meridie, et tunc consumuntur. Et similiter 



MATHEMATICAE IN PHYSICIS UTILITAS, 141 

calor naturalis in principio post cibum et potum resolvit vapores 
fortiter et facit somnum. Sed quando invaluit diu super 
cibum consumit eos, et homo evigilat. Nam vapores resoluti 
obstruunt vias spirituum et calorum venientium ad sensus 
a corde et capite, et ideo oportet ut quiescant sensus, et hoc est 
dormire. Et sic de omni virtute agente, cujus est proprium 
resolvere et consumere. Primo resolvit dum debilis est, et 
postea fortificata consumit. 

£t dicit Albumazar et alii concordant, quod luna facit Expiana- 
effectum consimilem in quartis oppositis. Nam dum luna est flo^^Jijie 
in quarta inter oriens et meridiem fit fluxus in illa quarta et in whenmoon 
quarta opposita, quae est inter occidens et angulum terrae, et opposite 
dum resolvit quando est in quarta inter angulum medii coeli q^iartcr. 
et angulum occidentis. Similiter refluit tunc mare ab angulo 
terrae usque ad angulum orientis. Sed non dant causam 
hujus rei; solum dicentes quod luna effectum in quartis 
oppositis habet consimilem. Sed quomodo operabitur luna 
ubi non est? et constat, per medium terrae non transeunt 
ejus radii. Ad hoc autem juvat nos multiplicatio reflexa. 
Nam proculdubio coelum stellatum aut nonum est densum per 
totum, nam visus noster stat ad alterum illorum, sed non 
terminatur visus nisi per densum, ad quorum alterum multi- 
plicati radii lunae existentes in quarta una reflectuntur ad 
quartam oppositam, et sic virtus lunae est directa in quarta 
una, et ejus reflexio in eodem tempore in quarta opposita. 
Solis autem virtus est nimis potens, et ideo ad quoscunque 
angulos cadat potest consumere vapores cito, quos resolvit. 
Aliarum vero stellarum virtus est debilis propter earum elon- 
gationem a terra, quamvis multo sint majores quam luna sit, 
et propter debilitatem non faciunt hujusmodi operationem, 
quamvis ad angulos diversos cadant earum radii ut lunae. 
Nec tamen hic intelligo, quod sit ebullitio cum fervore caloris 
ut in liquore super ignem, sed similitudo est quantum ad 
resolutionem vaporum quam fadt virtus lunae, aut per radios 
lucis, aut per radios suae naturae substantialis, aut per 
utrosque. Quando enim de nocte per radios stellarum, et in 
mane et in vespere per solem fit resolutio vaporum de terra 
et aqua, non propter hoc ebulliunt cum fervore, et tamen in 



142 OPERIS MAJORIS PARS QUARTA. 

maxima copia elevantur, et sunt nubes infinitae. £t ideo non 
oportet ut aquae maris ferveant in fluxu. 



Capitulum VII. 

In quo multiplicatio virtutum comparatur ad sanitatem et 
infirmitatem corporis humani. 

influence Mira ergo potestas est hujus multiplicationis cum omnia 
mys on*'^ fiant secundum leges ejus et occulta et manifesta. Et honim 
health and notitia non solum necessaria est in scientialibus^ sed utilitates 
magnas nobis praestat in corpore et in anima, si diligenter 
investigemus, nam valde utile est scire has leges in conserva- 
tione sanitatis. Quoniam cum non possumus vitare omnes 
incidentias specierum et virtutum rerum malarum et nocivanim 
sanitati, nec possumus semper aptare corpora nostra ad 
pleniores casus virtutum venientium a rebus salutiferis, semper 
tamen debemus esse solliciti ut rerum nocivarum virtutes non 
capiamus principales, scilicet rectas fractas et reflexas, sed 
accidentales si possumus, et si non possumus vitare omnes 
principales, saltem vitemus rectas, et si non omnes rectas, 
declinemus casum ad angulos rectos, et si non possumus saltem 
caveamus pyramidis breviores. Et hae considerationes habent 
locum, quando homo exponitur coelestibus impressionibus 
nocivis, ut soli in aestate, et lunae de nocte, quae exhaurit 
corpora. Unde multi mortui sunt non caventes sibi a radiis 
lunae. £t praecipue quando homo exponitur radiis Saturni 
et Martis, quoniam isti duo inducunt laesionem magnam et 
corruptionem in rebus, ut experientia docet. Similiter quando 
homo recipit species a locis corruptis et immundis, et quando 
multiplicantur species leprosorum et infirmorum et maxime 
illorum qui habent morbos contagiosos, nec non eorum qui 
habent malas complexiones^ et praecipue mulieris menstruatae ; 
quoniam si ipsa aspiciat speculum novum, apparet nubes san- 
guinea in speculo ex violentia menstrui inficientis, ut Aristoteles 
dicit in libro de somnis et vigilia sccundo^, et de serpentibus 

* De InsomMiiSf cap. a tray r&y naTa/xfp^icay rcuV ywat^l yivoiAivw d/ifikii/fwnw 
c2f r6 itdrawrpor ytvtrai r6 Iviwok^s rov h&irrpov otov y€f4kff atfMarwdrp, 



MATHEMATICAE IN PHYSICIS UTILITAS. 143 

et aliis rebus venenosis. Et maxime considerandum est 
istud, quando homines et animalia nascuntur, et habent desi- 
derium nocendi et animum malignandi. Nam ad hoc reducitur The evil 
fascinatio, unde quod habet virtutis capit ex hac causa, ^^* 
quoniam proculdubio tunc fit fortior impressio, eo quod 
natura obedit cogitationibus animae et desiderio, et excitatur 
ad fortiorem operationem, sicut Avicenna docet octavo de Ani- 
malibus ct quarto de Anima per exempla et experientias varias, 
et certum est hoc. Unde Solinus narrat in libro de mirabih'- 
bus mundi ^, quod in quadam regione aquilonari sunt mulieres 
habentes geminas pupillas in oculis, quae cum irascuntur 
interficiunt homines solo visu, de quibus dicit Ovidius, nocet 
pupilla duplex. £t maxime cavendum est ne partes nobiliores, 
sicut oculi et facies, exponantur hujusmodi speciebus: nam 
vidi medicum excaecari dum intendebat curae habentis infir- 
mitatem oculorum, propter multiplicationem speciei venientis 
ab oculis patientis. Oportet enim in istis nocivis uti magnis 
cautelis, et maxime quando malum est g^ave vel intolerabile. 
Sicut Alexander doctrina Aristotelis ut historiae narrant, 
basilisci speciem venenosam positi super murum civitatis ad 
interficiendum exercitum per corpora magna polita retorsit in 
eandem civitatem, ut per proprium destrueretur venenum. 
£t per contrarium aptatio corporis ad species rerum salubrium 
recipiendas, quanto efficacius potest homo, multum est utilis 
per omnem modum tam sanis quam infirmis. 

Capitulum VIII. 
De infinitate Materiae*. 

Quoniam autem diutius tenui persuasionem ut ostenderem, Matter 
quomodo in rebus mundi a parte suorum eflScientium et"^"*J[j^^ 

' Solinus probably livcd in the third century a.d. His work, CoUedanta 
Rentm Mentorabilium, is in the main a recast of Pliny. It is from his work 
rather than from that of Pliny, that such compilers as Isidore and Martianus 
Capella derived their information. 

' Cf. Opus Teriium, cap. 38, where this subject is fully treated. It is discussed 
at stiil greater length in that part of. Bacon^s encydopaedic work, entitled 
Communia Naiuruiium; copious cxtracts from which are given by Charles, 
pp. 369-389. 



144 OPERIS MAJORIS PARS QUARTA. 

generantium nihil potest sciri sine geometrica potestate, nunc 
volo breviter pertransire a parte materiae illorum, ostendendo 
quod necesse est verificare materiam mundi per demonstra- 
tiones in lineis geometricis explicandas, si potenter volumus 
errores infinitos evacuare. Multitudo vero philosophantium 
non solum in forma propria philosophiae, sed in usu theologiae 
dicit et asserit,quod una est materia numero in omnlbus rebus 
et quod solum est diversitas a paite formarum. 

* Et arguit ad hoc quod si excludamus per intellectum a 
materia coeli et lapidis formas eorum non est assignare per 
quod differant quod actus a forma dividit, ut dicit Aristoteles 
septimo Metaphysicae. Et in primo Physicorum ^ dicit quod 
omnia sunt unum in materia sed differunt in forma: et in 
secundo Metaphysicae dicit quod nihil est in materia distinc- 
tum. Et si materia plurificaretur sicut forma, quod materia 
erit communis et praedicabilis de pluribus sicut forma. Et 
allegant quod omne universale naturam formae habet. Nam 
partes definitionis ut dicit Aristoteles septimo Metaphysicae 
sunt formae ^ ; sed partes definitionis sunt per genus et dif- 
ferentiam et componunt speciem; ergo species est forma 
tantum sicut genus et differentia. Et constat quod reliqua 
duo universalia Porphiriana, id est proprium et accidens, sunt 
purae formae, quia sunt de predicamentis accidentium. Ergo 
omne universale est forma ; et ideo materia non habebit 
rationem universalis sed singularis erit et una in numero 
omnibus. Et per hujusmodi fundamenta et auctoritates male 
translatas nituntur persuadere. Sed hic est error infinitus. 
Nullus enim major est in veritatibus speculativis, quia hoc 
dato impossibile est servare rerum generationem, et igno- 
rabitur totus decursus naturae. Sed quod plus est, si hic 
error discutiatur, invenietur valde propinquus haeresi, aut 
omnino haereticus, quo nihil magis sjt profanum,quia sequitur 
necessario quod materia sit Deus et creator. Quod volo ad 

* From here to nituntur persuadere omitted in J. It has been restored from O. 

* i) y v\ri dyywTTos Ka$* ahr^v. Met. vi. lo, § 13. Cf. NaturaL Au^H. ii. i, 
%% II, la. The passage in NaiuraL Auscult i. 4, § i, appears to refer to the 
opinion of others. 

■ 'AAAd Tov k&ycv ft4pfj rcl tov tldovs /iovotf kaTiv, Met. vi. 10, $ la; cf. la, 
%% 4-9; alsovii. a, §8. 



MATHEMATICAE IN PHYSICIS UTILITAS, 145 

praesens ostendere solum per rationes geometricas ut promisi, 
quamquam rationes naturales et metaphysicae sunt copiosae 
et efficaces^ de quibus alias grandis scrmo potest fieri. £t 
necesse est propter sensum vulg^i, qui violentus est ubique. 

Dico ergo quod si materia potest esse una numero inlfso, ii 
duobus, eadem ratione in tribus et in infinitis. Nam consimile ™*ess 
argumentum facit Aristoteles in capite de vacuo in quarto infinite 
physicae, dicens ^, quod si aliquid unum et idem potest esse in and be 
duobus, tunc potest esse in tribus, et sic in infinitis ; sed quod ^q"i^aicni 
potest esse in infinitis habet infinitam potentiam. Ergo materia 
est infinitae potentiae quare et essentiae infinitae, ut probabitur, 
et ideo erit Deus. Sed consequentiae dictae non possunt con- 
tradicere, scilicet quod sequatur quod materia eadem possit 
esse in infinitis si essent, et ideo concedunt ei potentiam 
infinitam sed negant essentiae infinitatem, quia nihil habet 
cssentiam infinitam nisi Deus. £t cum arctantur in hac parte 
circa infinitatem potentiae, incipiunt verbis vacillare, dicentes 
quod potentia materiae est infinita, sicut potentia continui. 
Sed istud nihil est, quia haec potentia non est respectu actus 
infiniti, nec respectu infinitorum simul et in actu consideran- 
dorum, et ideo haec potentia non est actu infinita, sed potentia 
tantum. Sed potentia infinita in tantum datur materiae 
secundum dictam positionem, ut si essent actu infinita, posset 
materia eadem numero esse actualiter in illis infinitis. £rgo 
actualiter et intensive habet potentiam infinitam. Caeterum 
potentia continui non est similis potentiae divinae: quia 
potentia divina non habet arctationem et limitationem, quan- 
tum ad actualem existentiam in. pluribus et in infinitis. Ad 
quam non se extendit potentia continui, sed materiae con* 
ceditur illa eadem existentia in pluribus, et sic in infinitis, per 
auctoritatem et. demonstrationem Aristotelia Quapropter 
potentia materiae non est similis potentiae continui sed 
divinae. 

Caeterum aliter vacillant in hac parte dicentes, quod 
potentia materiae est passiva, et potentia divina activa. Hoc 
enim excluditur multis modis. Nam potentia passiva dicitur 
respectu transmutationis suscipiendae ab agente. Sed potentia 

I Nai, AuscuU. iv. 8, % 13. 
fVOL. I. L 



146 



OPERIS MAJORIS PARS QUARTA. 



Malhc- 
maticnl 

disproof. 



existendi in pluribus non hoc respicit, et ita differunt Item 
potentia existendi in pluribus simul quae non est arctata nec 
limitata attestatur summae nobilitati, et ideo datur Deo et 
animae quae est in pluribus partibus corporis tota. Sed Deo 
et animae non datur propter aliquam rationem patiendi, ergo 
nec materiae. Item quaecunque sit haec potentia, sive activa 
sive passiva, oportet quod substantia materiae sit infinita si 
haec potentia est infinita ; et si hoc, tunc materia est Deus 
vel aequalis Deo, quia nulla res habet substantiam et poten- 
tiam infinitam nisi Deus. 

Sit ergo potentia infinita A linea, et linea B sit ejus finita 
substantia, et C linea sit potentia aliqua finita, quae sit pars 

potentiae infinitae. De 
omni enim quanto dato 
contingit partem per intel- 
lectum abscindere, ut vult 
Aristoteles primo Coeli 
et Mundi, et D linea sit 
substantia ejus quod est 
C potentia ; multiplicetur 
ergo D quousque aggre- 
getur substantia quae sit 
aequalis ipsi B, hoc enim 
est possibile, quoniam D tt B sunt finita, et haec substantia sic 
aggregata sit E linea. Similiterque multiplicetur potentia C 
in tantum ut excrescat potentia proportionalis ipsi £^ et sit F 
Hnea, hoc enim est possibile, quia C et D sunt finita, et ideo 
potest ad utrumque addi in tantum, ut aggregata sint propor- 
tionalia, sicut Cet D. Sed /^potentia est finita, quia ex aggre- 
gatione finita nascitur, et habet substantiam £ aequalem ipsi 
B substantiae, cui correspondet A quod est potentia infinita ; 
ergo potentia F finita et A potentia infinita habebunt aequales 
substantias. Quare finitum et infinitum aequabuntur, quia 
aequalibus substantiis debentur aequales potentiae, et pars 
toti aequabitur, quoniam F est pars A sicut C, ut positum fuit 
a principio de C, et F crescit ex aggregatione finita C, quare 
F erit pars A, et ita pars aequabitur toti. 

Et ex hoc ultcrius sequetur, quod pars habebit majorem 



A 


Potentia infinita. 


B 


Substantia ejus finita. 


C 


Potentia finita para ipsius A, 


D 


Substantia potentiae C. 


E 


Substantia aequalis ipsi B substantiae 


F 


Potentia proportionalis ipsi E. 


G 


Potentia mijor quam F. 



MATHEMATICAE IN PHYSICIS UTILITAS. 147 

essentiam, et plus de essentia quam totum. Quoniam acci- 
piatur aliqua potentia finita major ipsa F^ et resecetur a 
potentia infinita quae est A, et sit G linea. Oportet ergo 
quod G potentia, cum sit major quam Fy habeat plus de 
substantia, seu fundetur in majori et nobiliori essentia, quam 
fundatur F potentia. Sed F habuit aequalem essentiam ipsi 
A^ ut probatum est. Ergo G habebit majorem quam A ; et 
ita parti respondet plus de essentia et nobih'us quam toti, quod 
est impossibile, Et etiam sequetur, quod finitum habebit plus 
de essentia sibi respondente quam infinitum ; et omnia haec 
sunt impossibilia. 

Item nuUum infinitum potest habere potentiam finitam. 
Ergo per oppositum nuUum finitum potest habere potentiam 
infinitam. Antecedens probatur per consimilem demonstra- 
tionem priori, quia sit a linea tllud infinitum, et b linea sit 
illa potentia finita. Accipia- 



SubsUntia infinita. 



Potentia finita. 



Substantia finita pars ipsius a. 



Potentia ipsius c 



Potentia aequalis ipsi b potentiae. 1 



Substantia potentiae e. 



tur aliquod finitum vel pars „ 
ipsius a et sit ^ linea. Ergo 
habebit minorem potentiam ; 
et sit d linea. Multiplicetur ^ 
ergo d quousque aequetur j 
ipsi ^,quod possibile est,quia 
utrumqueest finitum ; et ideo 
tantum potest addi ad d^ ut -^ 
aggregatum sit aequale po- 

tentiae quae est b ; et sit illud aggregatum e linea. Similiter 
ergo multiph'cetur ^, et addatur ei quousque poterit habere 
potentiam illam quae est e, et illud aggr^^atum sit / linea ; 
hoc enim bene possibile est, quoniam c substantia et d 
potentia ejus sunt finitae, et ideo si ad d tantum potest 
addi, ut fiat e potentia major quam d ad ^, tantum potest addi 
de substantia ut a^regatum excrescat, cui e potentia erit 
proportionalis, et illud aggregatum habebit illam potentiam. 
Sed e potentia est aequalis potentiae by ut probatum est. 
Ergo/quod est finitum, quia ex aggregatione finiti et infiniti 
nascitur, habebit potentiam aequalem ipsi a, quod est in- 
finitum. Quod patet esse omnino impossibile, et sequetur 
ex hoc, quod pars aequetur toti, scilicet F ipsi A^ et etiam 

L % 



148 



OPERIS MAJORIS PARS QUARTA. 



quod pars est major toto, ut patuit in priori ratione ; et quod 
finitum habebit majorem potentiam quam infinitum, ut patet 
in terminis, et haec omnia sunt impossibilia. 

Item si potentia materiae est infinita, sit haec potentia per 
A lineam designata infinitam, quae si dividatur in puncto a^ 
tunc partes divisae sunt aequales, quia utraque ab ipso puncto 
a vadit in infinitum. Signetur ergo punctus *, et puncta c 

^ I ! ! ! ! 

f d a b c 

et d. Partes ergo divisae sunt aequales, sed b af\n infinitum 
decurrens est major quam af per a b, Ergo b c linea in in- 
finitum extensa, est major quam af. Ergo est major aequali 
af^ quod est abc, Ergo pars est major suo toto. Quapropter 
impossibile est potentiam materiae esse infinitam. Nec est 
haec demonstratio applicanda divinae potentiae, eo quod non 
est divisibilis, sicut potentia materiae corporalis. Sicut vero 
radices a parte efficientis traxi ad exempla rerum naturalium, 
sic similiter possunt aliqua notari quae consequuntur materiam 
in rebus mundi, in quibus miranda geometriae potestas 
elucescit. Nam si materia mundi una esset numero, oporteret 
necessario, quod forma esset una numero, sicut posuerunt 
Parmenides et Melissus, contra quos Aristoteles primo libro 
Physicae et libro de generatione se opponit. Certo enim ex 
unitate materiae numerali sequitur illa potentia falsissima, 
quam prius eliminavi per leges fractionum. 



Are tbe 

celestial 

spheres 

con- 

tinuous I 

A line 

traversing 

their 

bonndaries 



Capitulum IX. 
An corpora se tangant in puncto. 

Quoniam autem pro hac positione sunt geometricae falsi- 
graphiae, quae omnem hominem possunt perturbare, ideo volo 
aliquas inferre. Si enim corpora sint diversa in hoc mundo, 
ut coelum et elementum, et imaginemur lineam transire per 
medium eorum, non secabunt illam lineam in diversis punctis, 
quia tunc longitudo linearis esset in medio, et ita superficialis 



MATHEMATICAE IN PHYSICIS UTILITAS, 149 

latitudo et profunditas corporalis, et sic corpus tertium a coelo is cnt in 
et elemento esset inter ea, quod falsum est. Ergo in eodem adSiccnt 
puncto intersecabunt lineam illam. Sed continua sunt quorum points. 
terminus est idem. Ergo sunt continua. Multorum et maxi- 
morum virorum fuerunt hic responsiones variae, et omnes 
adhaerebant isti parti, quod in diversis punctis intersecarent 
vel naturaliter vel mathematice, vel utroque modo, distin- 
guentes inter continuitatem naturalem et mathematicam 
secundum Averroem in quinto Physicae. Sed istud nihil est ; 
necesse enim est quod in eodem puncto lineae intersecent se, 
ut sit virga ferrea imaginata ; sed ille punctus non continuat 
corpora secantia, et ideo non sunt continua, sed partes virgae 
vel lineae transeuntis, de quarum continuatione non potest 
concludi corpora ^sse continua per quae transit virga ; sed si 
in diversis punctis virgae daremus sectionem, tunc necessario 
pars virgae,quae est corpus, esset media; et hoc est impossibile^ 
Item ai^i potest subtilius, quod quibuscunque corporibus in 
hoc mundo positis, si sint diversa et contigua, non continua, 
supraponatur vel supponatur tertium corpus, ad quod aequi- 
distanter ducantur lineae duae a mediis punctis datorum 
corporum. Si ergo illae lineae terminentur ad puncta diversa 
in tertio corpore, tunc pars illius corporis est media inter eas, 
et aequaliter semper distant et appropinquant, et ex altera 
parte in medio duorum corporum distabunt per corpus inter- 
positum, quod omnino est falsum. Ergo continuabuntur ad 
unum punctum in tertio corpore, et eadem ratione ad extremi- 
tates suas in conjunctione corporum positorum, quapropter 
unum corpus erunt quae posita sunt, quia unus punctus non 
potest esse in diversis corporibus. Et hic turbati sunt multi, 
nec est tempus renovandi opiniones singulorum, praecipue cum 
veritas pateat. Si dicatur quod in eodem puncto corporis 
terminabuntur illae lineae nec sint aequidistantes, quia non 
distant in a1iquo,eo quod corpora simul posita sunt sine medio, 
et quia omnis distantia tollitur, oportet quod ad unum punctum 
in tertio corpore terminentur, et quoniam duo puncta non 
habent aliquid longitudinis, quoniam non sunt quanta, ideo 
non faciunt distantiam aliquam sicut nec unus punctus. Unde ^^\ ^"^^ 

. , ... . luch pomts 

tantani mdivisionem important duo puncta simul juncta, sicut occupy no 



I50 OPERIS MAJORIS PARS QUARTA, 

more space unuiTi per sc positum, quia puncto addito puncto non crescit 
quantitas, et ideo possunt remanere diversa puncta in ex- 
tremitatibus duarum linearum simul junctarum in corporibus 
duobus sine medio, quamvis ad imum punctum in tertio 
corpore terminentur. Sed si in illis corporibus simul junctis 
ducantur duae lineae ab illis punctis infra corpora et descendat 
una linea super extremitates earum ad angulos rectos, necesse 
est per xiv primi Elementorum Euclidis quod lineae extensae 
in corporibus sint una linea continua. Ergo et corpora similiter, 
nam talis est sententia illius propositionis. 

Et ex hac propositione deceptus fuit Averroes quinto 

Physicae, et omnes sequentes ipsum, volentes quod una sit linea 

mathematica, et per consequens unum corpus mathematicum, 

quamvis diversa sint naturaliter. Nam, ut dicit ibi, contiguitas 

naturalis transit in continuitatem mathematicam ; sed hoc est 

impossibile, nam quantitas mathematica et naturalis idem sunt 

A maihe- secundum esse, et secundum rem, sed differunt solum sccundum 

Unc^and considerationem, quia geometer considerat lineam naturalem, 

a physicai non prout est in naturali materia, et ideo dicitur mathematica. 

oniy in the Et hanc candem lineam considerat philosophus naturalis, ut 

point of est in materia naturali, sicut in ferro, vel lapide, vel alia re 

view. ^ ' t 

naturali. Et quia eadem res est secundum esse, et secundum 
veritatem existendi, naturalis et mathematica, ideo si hic esset 
linea una vel corpus unum mathematice, tunc eodem modo 
esset naturaliter. Dico ergo quod hic sunt lineae secundum 
veritatem diversae et corpora similiter, nec hoc repugnat 
intentioni Euclidis. Nam non vult quod sit una continua, 
sed quod quantum ad angulos rectos faciendos duae tantum 
faciunt quantum una, postquam illae duae jacent in eadem 
directione longitudinis ac si ibi essent duae partes ejusdem 
lineae continuatae ; et sic intendit in pluribus aliis locis ubi 
accipit unam pro duabus, cum idem faciat ad suum propositum 
una sicut duae. Et hoc est quando loquitur de communi 
diflferentia superficierum vel communi sectione, eam enim 
vocat unam lineam, cum tamen in veritate sint duae : sed una 
obtinet earum potestatem, et ideo facilius loquimur de una, 
quam de duabus. 

Si tamen objiceretur, quod si quis ponat diversitatem in 



MATHEMATICAE IN PHYSICIS UTILITAS. 151 

corporibus, accipiantur igitur duae tabulae plaoae superficiei 
et circularis figurae» et elevetur una ab altera sub eadem 
figuratione, tunc aer citius repleret partes extcriores inter eas 
quam centrales. Quapropter esset vacuum in partibus interior* 
ibus ad tempus. £t hic multae stultitiae solebant dici. Nam 
aliqui dixerunt aerem in iostanti moveri usque ad centrum ex 
lege naturae universalis, ne fieret vacuum ; alii quod omnia 
corpora tangentia se in aere vel aqua habent superficies 
humidasy ut Aristoteles dicit secundo de Anima, et hanc humi- 
ditatem aeris vel aquae interceptam posuerunt rarefieri subito 
per totum, ne fieret vacuum. Sed hoc quod dicitur, ne fiat 
vacuum, est pura negatio ^. Nulla vero negatio pura est causa 
afiSrmationis ; et ideo responsiones hujusmodi sunt falsae. 
Propter quod dicendum est quod sub eadem figuratione non 
potest una ab alia elevari, sed oportet quod declinet una cum 
elevatur ab alia, et sic aer ingreditur paulatim. Hoc de plano 
potest quilibet experiri in scypho vitreo demisso in vas plenum 
aqua ; nam pro mundo non potest elevari in eadem figuratione 
suarum partium. Cujus causa est, ut aqua ingrediatur ejus 
locum paulatim. Et haec est afilirmativa ad quam ex conse- 
quenti excluditur vacuum. 

Si ergo oportet quod sint plures materiae corporales et Refutetion 
plura corpora in hoc mundo, cum quodlibet corpus est divisibile [^h^^^°I)f 
in infinita, non tamen propter hoc mundus erit compositus Demo- 
ex partibus materialibus infinitis, quae vocantur atomi, ut ^"'^*' 
posuerunt Democritus et Leucippus, quorum positione fuit 
Aristoteles magis impeditus et omnes naturales, quam per 
aliquid aliud erroneum. Quod tamen per geometricam potes- 
tatem eliminatur omnino ; nam nihil fortius potest argui contra 
hoc, quam quod tunc diameter quadrati et latus essent com- 
mensurabilia, id est, haberent communem mensuram, scilicet 
aliquam partem aliquotam pro communi mensura, cujus 
contrarium Aristoteles semper docet. Et patet per demonstra- 
tionem ex ultima parte septimae propositionis decimi libri 
Elementorum, per quam demonstratur, quod si aliqua mensura 

' A striking instance of Bacon*s positivity. No natural action takes place in 
order that some other action may not foUow. The remark is repeated in the 
next cbapter. 



152 



OPERIS MAJORIS PARS QUARTA. 



ut pes vel palmus mensuret costam, non mensurabit diametnim, 
nec e contra ; ut si diameter sit ex decem pedibus non erit 
costa ex aliquot pedibus. Et non solum sequitur ex hac 
positione, quod essent commensurabilia, sed aequalia. Quod 
patet evidenter in hac figura. Nam si latus habeat decem 

atomos, vel duodecim, vel plures, 
tunc trahantur tot lineae ab illis 
atomis ad totidem in opposito 
latere, et latera quadrati aequalia 
sunt; quapropter tot lineae occu- 
pabunt totam superficiem quadrati^; 
et ideo cum diameter transit per 
illas hneas, et non possunt plures 
assignari in quadrato, singulas capiet 
atomos a singulis lineis, et ideo non 
plures erunt in diametro, quam in 
costa, et sic habent partem aliquotam pro communi mensura, 
et tot partes habet costa sicut diameter, quorum utrumque 
est impossibile. 




FiG. 14. 



Capitulum X^. 



De figura mundi. 



rroafthat Quoniam vero necesse est corpora mundi esse plura, et 
^p^^J^/^divisibilia, et quanta, oportet quod figurationem habeant 
debitam, ad hoc ut mundus consistat. Figuratio vero est 
passio materiae, et invenitur in rebus ratione materiae, sicut 
KevoiutioD et quantitas. Nam figura uno modo est quantitas clausa 
J!ihCT^figure ^^**^^^ 5 *'*^ modo dicitur ipsa dausio quantitatis. Necesse 
would est vero mundum extra habere figuram sphaericam. Nam 
vacuum. quaccunque alia detur, accidet vacuum vd possibilitas ad 

> Thc &nacy lies in supposing that lines could occupy soperficial space ; as 
Bacott would have seen if he had tried to occupy the surface of thc square wilh 
small circles or squares. 

' Cf. Opus TrrtiMm, cap. 40^ 



MATHEMATICAE IN PHYSICIS UTILITAS. 153 

ipsum. Sed natura nec sustinet vacuum, nec possibilitatem 
respectu ejus. Si enim esset alicujus figurae angularis, tunc de 
necessitate accideret vacuum in moto suo : nam ubi modo esset 
unus angulus nihil esset donec alius ang^lus ibidem veniret ^ 
Figurae autem aliae quae maxime competerent essent vel ovalis 
figurae vel consimiles ei vel lenticularis et ei conformes se- 
cundum Aristotelem, libro Coeli et Mundi. Sed negat coelum 
habere hujusmodi figuram, sed causam non exprimit. Figura 
vero lenticularis est figura illius leguminis quod vocatur lens. 
Habet enim laterales superficies gibbosas, deficiens a vera 
sphaericitate propter breviorem diametrum quae transit per 
illa latera. Si vero esset figurae ovalis, aut pyramidalis 
rotundae, aut columnaris, aut alicujus hujusmodi, et moveretur 
super breviorem diametrum, adhuc accideret vacuum in actu, 
si vero super longiorem, non accideret vacuum in actu, sed 
possibile esset vacuum accidere, quoniam tanta esset possi- 
bilitas in mundo, quantum ad figuram ut moveretur super 
breviorem diametrum, sicut super longiorem. Si vero esset 
lenticularis figurae vel casealis, vel hujusmodi, et moveretur 
super longiorem diametrum, accideret vacuum in actu, et si 
super breviorem, non accideret in actu sed possibilitas relin- 
queretur. Nam aeque possibile esset mundo, quantum est de 
se, ut moveretur super unam diametrum sicut super aliam. 
Nec potest dici quod si esset ovalis figfurae moveretur semper 
super longiorem, et si lenticularis moveretur super breviorem, 
ne vacuum accideret. Refellendum est istud sicut superius, 
scilicet quod impossibile cst quod pura negatio sit causa 
alicujus affirmationis; sed, ne sit vacuum, pura negatio est. 
Et ideo oportet quod mundus sit sphaericae figurae, in qua Eqnality 
sola corporali sunt omnes diametri aequales, ut possit libere fj^^] ^^ 
volvi secundum omnem diametrum, et sic nullum sequitur 
inconveniens. Similiter intra necesse est, ut sit sphaericae 
figurae et concavae : nam planae figurae non potest. Quoniam 

' This is from AristoUe, De Coelo, ii. 4 cl y^ Urm ^M^ypa/ifun, av/x^trai 
itai rivw l^w cTvai maX cw/m uai icivw, K4ifX^ y^p aTp^S/uwoy t6 tifOiypaiJLiiov 
oMwoTf Hiv a^ri^ 4^ci X^pav, dXX' iwou fp&rtpov jfr aSiiMa^ rw oifK foTtUy «oi ov 
vw obx icTt, wA\iv ioTai M tV wa^Kka^iv tStv yoivtStv, 'Ofioims 8i ictar tXri Akko 
(rx9/ia yivotro ^i) taas ixov rds U rov lUcov ypaii§aas, otov faHO*i9ks 1j tpotiUs, 



154 



OPERIS MAJORIS PARS QUARTA. 



ducantur a centro terrae tres Imeae et una ducatur perpen- 
diculariter ad superiiciem coeli, ut a b, illa erit brevior aliis 
per xviii primi Elementorum et per xxxii ejusdem. Ergo 
coelum non aequaliter distabit a terra: sed oportet ut sit 
ejusdem naturae in omni parte. Ergo quaelibet nata est 
elongari aequaliter a terra. Nec potest esse convexa interius, 





C&NTRUM TERRAE 



CeNTRUM TERRAE 



FiG. 15. 



ut patct per viii tertii libri, quae dicit quod a puncto extra 
signato si ducantur ad circulum plures lineae, illa quae caderet 
in diametrum esset brevior aliis. Ergo relinquitur, quod si 
a centro terrae ducantur tres lineae ad convexitatem coeli, 
una erit brevior, scilicet illa, quae est perpendicularis super 
sphaeram, ut patet in figura, et ideo coelum non aequaliter 
distaret a terra, quod tamen oportet ut dictum cst. Et iterum 
si esset mundus convexae figurae, intra non esset natus 
continere omnia : sed mundus natus est continere omnia. 
Quod si non potest esse planae figurae, nec convexae, oportet 
quod sit concavae, cum non sit alia. Sed concava potest esse 
multis modis, aut sphaerica, aut columnaris, aut pyramidalis, 
aut lenticularis, aut alia multiplex. Non est autem possibile, 
quod sit alicujus nisi sphaericae concavac, propter hoc quod 
in hac sola figura sunt omnes lineae aequales, quae ab uno 
puncto ducuntur ad superficiem. Non enim est in aliis pos- 
sibile dare punctum,a quo omnes lineae ductae adsuperficiem 
aequentur: nam diametri sunt inaequales. Sed oportet partes 
coeli aequaliter distare a terra, propter naturae aequalitatem. 
Ergo de necessitate erit sphaericae. 

Item inter omnes figuras isoperimetras sphaera ipsa maxime 



MATHEMATICAE IN PHYSICIS UTILITAS. X55 

capit, sicut proponit viii propositio libri Isopcrimetronim^ Of figures 
Superficiales vero figurae dicuntur isoperimetrae, ut triangulus surfece thc 
et quadrangulus, et circulus, quando latera trianguli extensa ^P***'^ ^^^ 
in continuum et directum tantum habent in longitudine, content. 
quantum latera quatuor quadranguli extensa et quantum 
circumferentia circuli si extenderetur, et sic de quibuscunque 
figuris superficialibus. Unde dicitur isoperimeter ab laov quod 
cst aequale et v^pL quod est circum, et iurpov quod est meu'- 
sura, quasi aequalis circummensurationis. Et inter omnes 
istas superficiales isoperimetras circulus maxime capit, sicut 
dicit vii propositio de isoperimetris. Corporales vero tunc 
dicuntur isoperimetrae, ut sphaera, cubus, et columna, et 
quaecunque, quando superficies sphaerae extensa in con- 
tinuum et directum tantum habet in longum et latum 
quantum superficies sex ipsius cubi, et quantum supcrficies 
columnae rotundae, et sic de aliis. Sed inter omnes istas 
sphaera maxime capit, sicut demonstratur in libro supra- 
dicto. Cum ergo coelum debet omnia continere, oportuit 
quod esset sphaericae figurae. Item nobilitas mundi, et hujus 
figurae dignitas correspondent. Nam haec figura est prima 
figurarum corporalium, quia una superficie contenta, omnes 
autem aliae habent plures. Ergo competit corpori primo ut 
coelo. Item haec est simplicissima, quoniam sine angulis et 
cono et lateribus et onini diversitate. Ergo debetur corpori 
simplicissimo, quod est coelum. Item aptissima est motui. Spherical 
Ergo debetur priroo mobili. Item est elcngata ab occasionibus ad^ted 
et impedimentis, quia non habet angulum in quem aliquid for motion. • 
ofTendat. Ergo maxime competit corpori quod impedimentum 
et occasionem offensionis capere non potest. Item est per- 
fectissima, quia nihil addi potest ei ; sed omnibus aliis potest 
aliquid addi. Ergo corpori debetur perfectissimo. 

Quod autem corpora contenta in coelo habeant figuram The 
sphaericam, hoc demonstratur de aqua, quae jacet in medio, ^^thin the 

* The author of this book is Zenodonis, who probaUy belongs to the genera- 
tion succeeding that of Archimedcs. Its principal propositions. fourteen in 
number, are to be found in the fifth book of Pappus, and also in Theon's Com- 
mtntary oh the Almagtsi ofPtoUfny, See Cantor, vol. i. pp. 308-9, and 379-8o. 
Cantor shows, voL i. pp. 605 and 635 that Zenodorus was known to the Arabs. 



\ 



156 OPERIS MAJORIS PARS QUARTA. 

he:ivLns of ut pcf consequens pateat de aliis. Ducantur lineae undique 
form^^ ad superficiem aquae a centro terrae, planum est quod aqua 
Wnier. sempcr currit ad inferiorem locum propter suam gravitatem 
ut videmus. Ergo si una illarum esset brevior altera, aqua 
curreret ad extremitatem illius donec aequaretur. Ergo 
omnes lineas ductas undique a centro mundi ad superficiem 
aquae aequari necesse est Sed ad planum aequari non 
possunt, per xxviii et xxxii primi Elementorum, ut superius 
dictum est, nec ad convcxam per viii tertii. Ergo oportet, 
quod superiicies aquae continens terram sit concava, et 
non cujuscunque concavitatis, sed sphaericae, quoniam in 
sola illa iigura omnes diametri sunt aequales. Et haec de« 
monstratio non solum tenet de aqua interius, sed exterius. 
Nam exterius fluit ad inferiorem locum semper sicut interius. 
Et ideo oportet, quod sit convexa exterius, nam neque ad 
planam neque concavam exterius possent omnes lineae ductae 
a centro esse aequales, secundum formam demonstrationis 

prioris, et hoc patet per ex- 
perimentum. Nam sit navis 
g d^ et portus ^, et c sit 
superficies navis ubi figitur 
malus, et b sit extremitas 
mali, et ducatur c a linea perpendiculariter a portu ad extre- 
mitatem mali. Planum ergo est per xix et xviii primi 
Elementorum quod a b linea est longior quam c a. Ergo si 
mare esset planae figurae, tunc oculus existens in c videret 
portum melius, quam existens in ^, quoniam b plus distat ab 
a quam c, Sed per experientiam scitur, quod ille qui est in 
summitate mali potest videre portum citius quam ille qui est 
in superficie navis. Ergo relinquitur quod aliquid impedit 
visum illius qui est in navi. Sed nihil potest esse, nisi tumor 
sphaericus aquac. Ergo est sphaericae figurae. Sed si hoc, 
tunc terra est sphaericae figurae convexae, nam aliter non 
elongaretur aequaliter a coelo, neque appropinquaret centro 
mundi aequaliter ; sed hoc oportet fieri. Item esset vacuum 
ubi se non contingerent: quoniam si esset planaevel concavae 
non contingeret concavitatem aeque, ut patet, et ideo vacuum 
esset inter eas. 




FiG. 16. 



MATHEMATICAE IN PHYSICIS UTILITAS, 157 

Similiter de sphaericitate aeris concava intra et extra, Air. 
omnino negotiandum est sicut in prima demonstratione de 
aqua ; quia aer est gravis ^ in sphaera sua sicut aqua, ut prius 
habitum est, et ideo currit ad inferiorem locum. Et praeterea 
vacuum esset inter aerem et aquam, si aer esset alterius iigurae. 
Nam, si esset planae, tunc non tangeret aerem nisi in puncto, 
per tertiam primi libri Theodosii ; quia sphaera non tangit 
planum nisi in puncto, ut ibi dicitur. Si vero convexae, iterum 
non tangit nisi in puncto per duodecimam tertii Euclidis. 
Nam signentur duo circuli in sphaera aquae convexa, et aere 
convexoy non se tangent illi circuli nisi in uno puncto, sicut 
probatur in illa duodecima. Ergo nec corpora in quibus 
signantur ; nam si corpora se tangerent in pluribus locis, et illi 
circuli, ut patet ad sensum. Et ita oportet, quod utroque modo 
sit vacuum. Et si esset alterius concavitatis quam sphaerae, 
non omnes lineae ducerentur ab uno puncto ad superficiem 
corporis aequales. Igitur oportet superficiem aeris esse 
sphaericam intra et extra. 

Deinde patet per has demonstrationes ultimas de igne, sicut Fire. 
de aere. Sed illa quae vadit per descensum ad inferiorem 
locum non tenet hic, quia ignis non est gravis in sphaera sua. 
Oportet tamen omnes lineas ductas a centro mundi ad super- 
ficiem ignis esse aequales, quia ignis est contrarius terrae et 
summe leve, et ejusdem naturae in toto et partibus singfulis. 
Quapropter aequaliter elongatur a loco gravium, et a centro 
mundi, et hoc exterius et interius. Ergo oportet quod sit 
concavus intra, et convexus extra, et hoc sphaerice, sicut 
priora concludunt. 

Capitulum XI. 

Quod plus aquae contineat vas inferiori quam superiori loco 

positum. 

Sed nunc per figuram aquae magnum naturae miraculum A vessei 

filled with 
^ The vitfw as to Uie gravity of air deserves notice. It was maintained how- 
ever by AristoUe. Cf. Di Coeh, iv. 4, § 5. Ether, or fire, on the contrary, 
was regarded as imponderable, as the nezt paragraph shows. 



centre. 



158 OPERIS MAJORIS PARS QUARTA. 

watervaries potest suscitari ; quoniam si scyphus continens aquam ponatur 
^cording ^^ '^^^ inferiori, poterit plus capere de aqua, quam in loco 
to distarice superiori, ut in cellario et solario. Nam propter inclinationem 
carth*s naturalem aquae ad centrum mundi ubicunque sit, sive in 
loco superiori, sive inferiori, partes ejus semper currunt ad 
inferiorem locum ; et ideo per lineas aequales semper distant 
a centro, et ideo oportet semper quod pars superior aquae sit 
portio unius sphaerae describendae circa centrum mundi, licet 
in fundo scyphi retinet figuram vasis, quia ibi solum tangit 
vas et non superius. Quare pars suprema figurabitur secundum 
legem gravitatis aquae, et hoc est respectu centri mundi, et 
ideo superior pars erit portio sphaerae imaginandae circa 
centrum mundi. Sed constat quod in loco inferiori erit 
portio minoris sphaerae et in superiori portio majoris, quia 
magis tunc distabit a centro ; nam sphaera superior continebit 
inferiorem, ut patet in circulis circa idem centrum. Diameter 
autem scyphi erit chorda utriusque portionis, si scj^hus 
impleatur utrobique quantum potest capere. Ergo iUa diameter 
resecabit de majori sphaera minorem portionem, et de minori 
majorem. Et per xxxviii propositionem triangulorum 
Jordani^, in circulis inaequalibus eadem chorda resecat de 
majori circulo minorem poitionem, et de minori majonem, et 
ita erit de sphaeris. 

Nam signentur illi circuli in sphaeris 

illis, et portiones circulorum in por- 

tionibus sphaerarum, et patet quod 

idem est. Ergo portio aquae super 

diametrum scyphi erit major, quando 

vas est in inferiori loco, quam quando 

est in superiori, et ideo gibbositas 

major et tumor altior ; quare oportet 

quod plus de aqua ibi sit, si scyphus 

^^^* *^' sit omnino plenus, quam quando est 

in superiori loco. Quapropter ad eandem aquam potest plus 

infundi de aqua in scyphum, quando est inferius, quam 

quando est superius. Nam inferius aqua quae est super 

' See note on this writer in chap. 16, p. 169. 




MATHEMATICAE IN PHYSICIS UTILITAS. 159 

diametrum scyphi contrahet se a lateribus vasis, et coan- 
gustabit se in portionem minoris sphaerae, quia propinquior 
est centro mundi, et ideo chorda ejusdem aquae fiet minor, 
quam quando fuit superius. Et erit pars diametri scyphi 
ejus chorda, non tota diameter, sed ex utroque latere 
abscindetur aliquid de diametro, ut residuum fiat chorda 
portionis aquae. Quapropter in lateribus aquae a loco ab- 
scissionis diametri usque ad vas erunt duo spatia parva, ubi 
poterit plus de aqua infundi quam quando est in superiori 
loco. Et hoc totum facit inclinatio aquae secundum i^em 
suae gravitatis figurantis se secundum sphaeram minorem et 
majorem respectu centri mundi ; cum tamen vulgo studentium 
videatur hoc esse omnino impossibile, imo magnis viris qui 
geometriae nesciunt potestatem. 



Capitulum XII. 

An figurae quinque corporum regularium mundo con- 
veniunt, ut voluerunt Platonici. 

Ex istis vero figurationibus sphaericis corporum mundi piato's 
aperitur magnum fundamentum in certificatione rerum natur- ^**' ^^ 
alium, et evacuantur violentae falsitates. Nam Platonici \ in dcnce of 
quorum tempore viguit geometria, ut Averroes dicit tertio j^^^^^^ 
Coeli et Mundi, aestimaverunt quod corpora mundi prindpalia, elements t<> 
scilicet coelum et quatuor elementa, figurarentur figuris quinque regular 
corporalibus quae regulares vocantur, et sunt aequiangulae et «o"^»- 
aequilaterae et inscriptibiles spherae et circumscriptibiles 
eidem, et nullae aliae. Et propter has causas sunt nobilissimae 
figurarum praeter sphaeram, quas lator praesentium de facili 
potest praesentare, et sunt tres ex superficiebus triangularibus, 
et quarta ex quadratis, et quinta ex pentagonis; et non 
possunt esse plures, quod est mirabile. Prima habet quatuor 
superficies triangulares, et vocatur tetraedruni a r^rpi^ quod 

' See TimantSf 54. It does not appear that Bacon had read Plato. 



i6o OPERIS MAJORIS PARS QUARTA. 

est quatuor, seu pyramis quatuor basium triangularium. 
Secunda habet superiicies octo triangulares, et ideo vocatur 
octaednjm,nam octo purum est Graecum, non Latinum. Tertia 
habet viginti superficies triangulares, et vocatur icosaedrum. 
ab €Uo<n quod est viginti. £t non possunt esse plures fig^rae 
regulares ex basibus triangularibus. Nam nuUus angulus 
corporalis potest valere quatuor rectos superficiales, ut docet 
xxi undecimi libri Elementorum. Sed sex anguli triangu- 
lorum aequiangulorum valent quatuor rectos : nam tres valent 
duos rectos, ut patet ex xxxii propositione primi libri quae 
vulgata est. £t ideo sex anguli triangulorum non possunt 
componere angulum corporalem ; et ideo nec figura corporalis 
potest fieri ex superficiebus triangularibus, quarum sex anguli 
semper concurrant ad angulum unum corporalis figurae. Sed 
bene potest fieri, quod quinque anguH vel tres triangulonim 
constituant minus quam quatuor recti. £t si ex tribus angulis 
triangulorum constituatur angulus corporalis, tunc oportet 
quod sint quatuor superficies triangrulares in corpore illo. 
£t si ex angulis quatuor triangulorum fiat angulus corporalis. 
tunc oportet quod sint octo trianguli in figura corporali. Si 
vero quinque anguli triangulorum faciunt angulum corporalem, 
tunc oportet quod in figura corporali sint viginti superficies 
triangulares undique, ut patet ad sensum in figuris corporali- 
bus. £x duobus autem angulis superficialibus non potest fieri 
angulus corporalis, quia omnis angulus talis est ad minus ex 
tribus superficialibus, ut dicit £uclides in principio xi ; et qui- 
libet geometer scit hoc. £rgo tantum tria corpora regularia 
erunt ex triangulis. £x quadratis vero non potest esse nisi 
unum ; nam angulus quadrati rectus est, et ideo tres tantum 
tales congregati possunt facere angulum corporalem, quia si 
quartus addatur jam non potest essc angulus corporalis, quia 
omnis angulus solidus est minor quatuor rectis. Sed si trcs 
anguli quadratorum concurrant ad angulum solidum, tunc in 
corpore constituto erunt sex superficies quadratae, ut est in 
taxillo ; et vocatur haec figura cubus et hexaedrum ab f£ 
Graece, quod est sex Latine. Si vero accipiantur anguH 
pentagonorum regularium, tunc tres faciunt angulum solidum, 
et non plures, quia si quatuor acciperentur, jam esset plus 



MATHEMATICAE IN PHYSICIS UTILITAS. i6i 

quam quatuor recti, eo quod angulus pentagoni est et rectus 
et quinta recti, ut patet ex xxxii propositione primi 
Elementorum, et sic essent ibi quatuor recti et quatuor 
quintae. Sed omnis angulus corporalis est minor quatuor 
rectis. Ergo tantum erit una figura corporalis ex pentagonis 
superficiebus, et oportet quod habcat duodecim superficies 
pentagonas, sicut patet in fabricatione illius corporis, et hoc 
vocatur dodecaedrum, id est, figura corporalis duodecim 
basium pentagonarum aequilaterarum. 

Et omnes istae figurae corporales regulares fiunt ex super- 
ficiebus regularibus quae sunt aequiangrulae et aequilaterae. 
Non est autem possibile quod ex superficiebus hexagonis fiat 
ah'qua fig^ra corporalis regularis, quia nullus angulus corporalis 
potest fieri ex angulis talium hexagonorum, propter hoc quod 
angulus talis hexagoni valet rectum et tertiam recti, ut patet 
ex xxxii primi Elementorum. Ergo tres tales faciunt tres 
rectos et tres tertias unius recti, sed tres tertiae valent integrum. 
In nuUa enim re possunt esse nisi tres tertiae. Ergo tres 
anguli hexagonorum regularium valent quatuor rectos, sed 
nullus corporalis valet quatuor rectos. Ergo nulla figura 
corporalis potest fieri ex superficiebus hexagonis, et longe 
minus ex heptagonis et octogonis et supra, quia majores 
angulos obtinent quam hexagoni. 

Quoniam vero dodecaedrum patitur in se inscriptionem 
omnium aliarum, ut patet ex quinto decimo libro Elemen- 
torum, ideo dederunt Platonici hanc figuram partibus coeli, 
propter hoc, quod coelum noscitur omnia continere. Unde 
dixerunt partes coeli concurrere in punctum unum secundum 
hanc figuram, ut constituatur corpus coeli. Et quia ignis 
ascendit in figura pyramidali, ideo dederunt partibus ignis 
talem figuram. Quoniam autem octaedrum maxime assimi- 
latur pyramidi, et aer praecipue assimilatur igni, dederunt ei 
figuram illam. Sed quoniam partes aquae revolvuntur an- 
fractibus et fluxibus multifariis, ideo dederunt ei figuram 
icosaedrum, quae multiformitate laterum et angulorum 
circumvolvitur in sphaera. Partibus vero terrae cubum 
dederunt, quia illa figura stabilis est et fixa inter omnes, sicut 
terra inter mundi corpora stabilitatem obtinuit et fixioncm. 

VOL. I. M 



i62 OPERIS MAJORIS PARS QUARTA. 

Arisiotie's Sed Aristoteles venit contra istos in tertio Coeli ct Mundi^, 
thirv^ua ^^ probat, quod ex hac figuratione vacuum erit in sphaera 
wonid be aquac, et in sphaera aeris, et in sphaera coelesti. Nam solus 
cubus et pyramis possunt locum replere, quando congr^antur 
circa punctum unum. Nam replere locum est duobus modis ; 
uno, sicut dicimus vulgariter, quod omne corpus replet locum, 
nisi sit instantia in ultimo coelo. et sic non accipitur repletio 
loci in proposito. Alio modo dicitur ess^ repletio loci non 
solum corporaliter, sed superficialiter, et magis quia paucitas 
superficierum implentium sua loca est causa paucitatis cor- 
porum replentium sua loca, ut dicit Averroes super tertium 
Coeli et Mundi. Replere vero spatium superficiale est implere 
quatuor angulos rectos, quia non possunt plures esse circa 
punctum unum in superficie, ut patet ex intersectione duarum 
linearum ad angulos rectos hoc modo. Et sic quadrata pro- 
priissime possunt locum replere superficialem, scilicet quatuor 
quadrata, quia angulus quadrati rectus est, et sex trianguli, 
quia sex anguli tales valent quatuor rectos, et tres hexagoni, 
quia eorum anguli tres valent quatuor rectos, ut prius tactum 
est. Sed pentagoni non possunt locum replere, quia tres 
anguli eorum valent tres rectos et tres quintas, et hoc totum 
minus est quatuor rectis, et quatuor anguli pentagonorum valent 
quatuor rectas et quatuor quintas, quod est plus quatuor rectis, 
et ideo haec figura regularis non potest locum replere. Similiter 
nec heptagonus, nec aliqua alia, ut patet. £t ideo tantum 
tres superficiales locum replent Et propter hoc paucae erunt 
corporales, quae locum replebunt corporaliter, et hujusmodi 
repletio corporalis non est per unum corpus, sed quando plura 
corpora congregantur circa unum punctum undique, ita ut 
impleant spatium corporale circa illud punctum. Et hoc 
spatium habet octo angulos corporales, et duodecim angulos 
superficiales rectos distinctos secundum rem, licet sint viginti 
quatuor secundum rationem, quoniam quilibet angulus cor- 
poralis est ex tribus superficialibus, et ideo quoad hoc compu- 
tantur ter octo, qui sunt viginti quatuor. Sed saepe iterantur 
aliqui, quia hi anguli sunt conjuncti; si enim essent divisi, 

^ De Coehj iii. 8, § x ^OKw 8i rd wdpatrSai rd dwkSi a^/mra ax^/iaT[(€tv 6X!oy69 
IffTi, wpSfToy tihf 6ri ffvftfi^frfrai ^ dvawKifpwcBai t6 6kor, 



MATHEMATICAE IN PHYSICIS UTILITAS. 163 

tunc oporteret esse viginti quatuor^ secundum veram distinc- 
tionem, ut quilibet angulus corporalis ab alio distinctus haberet 
tres rectos sibi proprios. Omnia haec patent ex tribus lineis 
intersecantibus se ad angulos rectos, ut in tribus festucis vel 
aliis. Quoniam vero angulus cubi est ex tribus rectis, ideo 
octo tales possunt propriissime replere locum circa jpunctum 
unum. Et ideo in sphaera terrae secundum figurationem nunc 
dictam, non erit vacuum, quia octo cubicae partes terrae con* 
gr^atae circa centrum mundi replent locum totum necessario 
circa illud centrum. Angulus vero pyramidis est ex tribus 
angulis triangulorum, quapropter valet duos rectos, et ideo 
anguli sex tales valent quatuor angulos cubicos, nam utrobique 
valent duodecim rectos, et alii sex valent alios quatuor angulos 
cubicos. Quapropter concludit Averroes in tertio Coeli et 
Mundi, quod duodecim anguli pyramidum congregati circa 
punctum unum implebunt totum locum corporaliter, sicut 
octo cubici anguli, et ideo in sphaera ignis non est vacuum. 
Sed aliae figurae congregatae circa punctum unum non 
possunt secundum Aristotelem et Averroem replere locum. 
Quotquot enim congregarentur habebunt majus vel minus octo 
angulis cubicis, et ideo locum non replebunt. Et ideo in 
sphaera aquae et aeris et coeli accidit vacuum necessario 
secundum figurationem Platonicorum. Sicut vero cubus in 
corporali repletione respondet quadrato in superficiali, quia 
cubus sit ex quadratis superficiebus, propter quod utraque 
figura propriissime replet locum,sic pyramis respondet triangulo 
regulari, quia fit ex triangulis, et utraque figura locum replet. 
Sed tertiae figurae, scilicet hex^ono superficiali, non respondet 
figura corporalis replens locum, quia ex superficialibus hexa- 
gonis non potest figura hexagonalis rcgularis constitui, ut 
demonstratum est prius. 

Et tamen apis facit domus hexagonas ne vacuum inter- Hexagon 
cipiatur ; et natura in ventre terrae generat crystallos omnes ^^^ '^^ 
hexagonas in unum congregatas. Et sic lapides, qui vocantur >n crysul. 
irides et in insulis Hibemiae et India dicuntur ab autoribus 
inveniri, congr^antur in figura hexagona. Et dicuntur lapides 
iridis, quia repraesentant colores iridis et arcus coelestis, quando 

» J. has XV, 
M 2 



i64 OPERIS MAJORIS PARS QUARTA. 

ponuntur ad radios solares. Et sic est de omnibus generatis 
in hoc mundo, quae per superficies suas congregantur, ut 
retineant figuras hexagonas, ut vacuum excludatur, et hoc est 
mirabile. Sed tamen non est vera loci repletio secundum 
quod Aristoteles accipit in hoc loco : nam talis est secundum 
omnem situm corporum et superficierum, ut taxilli quatuor 
superficialiter secundum omnem situm replent locum, et octo 
corporaliter, qualitercunque mutentur anguli vel latera, nam 
aequalitas plena est in illis angulis et lateribus. Et sic est dc 
pyramidalibus corporibus, et de triangulis superficialibus et 
quadratis et hexagonis. De aliis non contingit hoc secundum 
omnem situm sed secundum aliquem, et ideo hic non com- 
putantur. Nam si aliquibus domibus apum erectis aliae 
ponantur secundum alium situm, non est loci repletio, sed 
vacuum spatium relinquitur, et ideo non sunt de replentibus 
locum, ut absolute et simpliciter dicatur repletio. Magna est 
ac profunda consideratio de his figuris replentibus locum 
propter rerum naturalium figurationem. Sed quantum suflScit 
ad praesens in universali de hac figuratione in corporibus 
mundi principalibus declaravi. 



Capitulum Xlir. 

An possint esse plures mundi, et an materia mundi sit 
extensa in infinitum. 

If there Et transeo ulterius ad duo exempla breviter annotanda in 

rnWeS» corporibus mundi, quae fundatur super geometricam potes- 

a vacuum tatem, et sunt adhuc annexa materiae corporali eorum. Nam 

left. Aristoteles dicit primo Coeli et Mundi *, quod mundus occupat 

totam suam materiam in uno individuo unius speciei, et sic 

de quolibet corpore mundi principali, quoniam unus mundus 

est numero, nec possunt plures mundi esse in hac specie, 

sicut nec plures soles nec plures lunae, licet multi posuerunt 

contrarium. Nam si esset alius mundus, esset sphaericae 

4 

jf^ * Cf. OpMs Tertium, cap. 41. 

* D€ Coeh, i. 9 l£ Awdatjs y&p lcrt 7^5 ofirccas Ckrfs 6 iroi k6cijuk. 



MATHEMATICAE IN PHYSICIS UTILITAS. 165 

figurae, sicut iste, et non potest esse distantia inter eos, 
quia tunc spatium vacuum sine corpore esset signabile inter 
iUos, quod falsum est. Quapropter oportet ut se tangerent, 
sed non possunt tangere se nisi in puncto uno per xii 
tertii Elementorum, ut prius declaratum est per circulos. 
Ergo alibi quam in illo puncto erit spatium vacuum inter 
eos. Aliud est, quod corporalis materia mundi non est 
extensa in infinitum, ut multi posuerunt. Nam geometrica 
potestas hoc excludit, Quoniam conjungantur^ duae lineae 
a et b angulariter in centro mundi, et a concursu earum 
extendantur in infinitum, et tertia uni illarum ducatur aequi* 
distanter et terminetur ad aliam, .et sit ca. Ergo ^ et ^ 
sunt aequales, et Oy quae est pars ^, et c sunt aequales, quia 
ab eodem puncto scilicet vadunt in infinitutn. Sed c linea 
aequatur b lineae. Ergo o linea aequabitur ipsi a totali, 
scilicet pars suo toti, quod est impossibile. 



Capitulum XIV ^ 

De unitate temporis. 

Multae autem aliae demonstrationes geometricae possent 
ad hoc adduci, atque veritates aliae in rebus mundi possent Time con- 
notari quasi infinitae, in quibus geometrica virtus elucescit ^ "^^ 
Sed haec suflficiunt persuasioni, et solum evacuabo duas fal- matter, 

. , , . . , , butwith 

sitates, quae ad unitatem matenae numeralem consequuntur motlon re- 
secundum opiniones vulgatas. Nam ponunt quod tempus sequi- ^"^**^ 
tur ad materiam rerum, et aevum ad formam, et ideo sicut of one 
materia est una numero et non plures, sic tempus est unum *™*""*^"' 
numero simul et semel, et sicut forma variatur in rebus, sic 
aevum multiplicatur in aevitemis. Unde plura dicuntur esse 
aeva, et unum tempus, ut secundum numerum angelorum sit 
numerus aevorum. Sed cum probatum est quod materia non 
potest esse una, tunc falsum est tempus habere unitatem ab 
ea. Deinde tempus non potest sequi, nisi ad subjectum suum. 

^ The diagram in O. has been omitted as unintelligible. 
' Cf. Ofms TerHumy cap. 41, which contains an application of the view here 
stated to the doctrine of Transubstantiation* 



i66 OPERIS MAJORIS PARS QUARTA. 

Sed motus est subjectum suum, non materia ; et subjectum 
motus non est materia, sed corpus compositum ex materia 
et forma. 
Thepresent Postremo res geometricae nobis ostendunt causam unitatis 
^!?^*^^' in tempore, et demonstrationem addunt super hoc. Nam 
point, may corpus quia habet undique dimensionem, ideo non compatitur 
to any secum aliud corpus : ubique enim habet corpus, unde aliud 
numberof excludat secundum longum et latum et profundum. Ergo 

roottons. ** 1- o 

superficies secundum longum et latum excludet aliam super* 
ficiem, sed non secundum profundum, quia sic est indivisibilis 
et caret dimensione. Et linea secundum longum excludit 
aliam, sed non secundum latum et profundum quia sic non 
habet dimensionem. Ergo punctus cum omni careat dimen- 
sione, non habet unde excludat aliud a suo loco indivisibili ; 
sed imaginato primo puncto in suo loco secundus adveniens 
habebit eundem locum in mente, quia non est distantia media, 
et sic de tertio puncto, et de infinitis. Motus vero non habet 
nisi linearum dimensionem a priori in posterius secundum longi- 
tudinem spatii, et hoc est a praeterito in futurum. Ergo solum 
secundum hunc decursum, scilicet a priori in posterius, seu a 
praeterito in futurum, unus motus excludet alium, scilicet prior 
posteriorem, et praeteritum excludet futurum. Sed comparatio 
motus ad praesens est alia quam secundum decursum a 
praeterito in futurum. Ergo respectu praesentis nullus motus 
habet dimensionem nec divisibilitatem, et ideo non habebit 
unde excludat alium a praesenti. Et ideo infinitos secum 
potest pati praesentes ; et ideo unum tempus praesens sufficit 
omnibus motibus praesentibus, et propter hoc habetur hic 
vera causa unitatis temporis, et non propter materiam. Ddnde 
ex istis elici potest unitas vera aevi, sicut temporis. Nam 
aevum vel solum habet dimensionem linearum, si ponamus 
aevum esse divisibile et habere partes, ut multi aestimant 
contra totam philosophiae potestatem, atque contra Augus^ 
tinum et Dionysium, quanquam Anselmus velit contrarium, 
Et si hoc sit verum, tunc ^ sic est de aevo sicut de tempore, 
propter quod erit unum et non plura. Aut aevum erit indi- 
visibile, et tunc erit ad aevitema, sicut locus indivisibilis ad 

» ncc, J. 



MATHEMATICAE IN PHYSICIS UTILITAS. 167 

puncta et atomos, et idem numero est locus unius puncti et 
plurium, ut prius habitum est. Ergo unum erit aevum omnium 
aevitemorum, et hoc est necessarium, et nuIH perito in philo- 
sophia dubium. Nec est contra sanctos et doctores principales, 
sed conveniens sententiae eorum. 



Capitulum XV. 

An motus gravium et levium excludat omnem violentiam. 
£t quomodo motus gignat calorem. Itemque de duplici modo 
sciendi. 

Quoniam vero motus est subjectum temporis, et tempus est in a faiiiiig 
mensura motus, possumus adhuc videre magnam geometriae ^^j^^^ 
potestatem in motibus corporum istius mundi. Aestimant point aione 
vero naturales, quod motus gravium deorsum sit naturalis f^^^th. 
omnino, et motus levium sursum est similiter omnino naturah's, 
ita ut non habeant de violentia. Sed figuratio geometrica 
ostendit nobis contrarium. Nam sit d b c lignum vel lapis in 
aere, et a centrum mundi, g h diameter mundi. Cum ergo 
db c sint semper in suo toto aequaliter distantes descendant 
ad centrum per lineas aequidistantes. Ergo d descendet per 
lineam de^et b per lineam b ayCt c per lineam co^ quapropter 
^cadet extra centrum mundi in diametro A^ versus coelum, 
scilicet in e puncto, et c in o, quare 
in hoc descensu d declinabit a centro 
a versus centrum per altttudinem a e^ 
et c per altitudinem a o. Sed omnis 
declinatio gravis a centro versus cen- 
trum est violenta, Ergo d et c mo- 
ventur violenter, et sic de omnibus 
partibus d b c praeter b quae sola 
vadit in centrum. Quapropter mul- fjg, ,8. 

tum erit hic de violentia. Caeterum 

incessus rectus et naturalis ipsius d est per lineam d a, unde si 
separetur d a suo toto caderet in a per rectum incessum, quia 
omne grave tendit in centnim. Omnis autem declinatio 




i68 OPERIS MAJORIS PARS QUARTA. 

gravis ab incessu recto est violenta, sed quanto magis d 
movetur super lineam d t, magis recedit ab incessu recto, ut 
patet ad sensum, quia d a et d e lineae magis separantur 
inferius quam superius. Ergo d quanto magis descendit 
deorsum, tanto magis movetur per violentiam, et similiter c, 
et ideo quaelibet pars ipsius totius d 6 c gravis, praeter d quae 
sola semper descendit secundum incessum rectum. Mani- 
festum est ergo quod magna et multiplex violentia est in 
motu naturali ipsius gravis. Et ex hoc sequitur quaedam 
veritas in rebus naturalibus, scilicet quod motus naturalis 
generat calorem; nam quum demonstrata est violentia, et 
constat grave naturaliter inclinari deorsum, planum est quod 
duae virtutes sunt in gravi moto deorsum inclinantes ipsum 
in partes contrarias. Ergo una distrahit partes gravis in unam 
partem, et alia in aliam, et ad has distractiones necesse est 
rarefieri partes gravis. Sed rarefactio est dispositio immediata 
ad calorem, unde per experientiam scimus quod grave de- 
scendens deorsum calescit. Potest ergo hoc hic adverti, sicut 
in prioribus, quod causae rerum naturalium debent assigrnari 
per mathematicae potestatem. Et potest homo videre quod 
in rebus naturalibus sunt duo modi arguendi, unus per de- 
monstrationem quae procedit per causas, et alius per demon- 
strationem ad effectum, ut cum prioribus demonstrationibus 
probatur per causam, quod violentia accidit gravi in suo motu 
naturali, postea demonstratur hoc idem per effectum, scilicet 
per generationem caloris. Nam non generaretur calor nisi 
per rarefactionem, nec rarefactio ista nisi per virtutes dis- 
trahentes grave in partes contrarias, et hae non possunt esse 
nisi una naturalis, altera violenta, quapropter grave in suo 
motu naturali habet violentiam. Et sic haec conclusio, grave 
recipit violentiam in suo motu naturali, probatur per causam 
et effectum. Sed causa sola facit scientiam aut longe majorem 
quam effectus, quia Aristoteles dicit primo Posteriorum quod 
scire opinamur cum causas cognoscimus. Ergo cum demon- 
stratio, ut ibidem docet, est syllogismus faciens scire, necesse 
est quod demonstratio per causam sit longe potentior, quam 
per effectum; et hoc vult Aristoteles libro Posteriorum '. 

^ £t . . . posteriorum, om. in O. Cf. AnaL Post. i. a, ( i. 



MATHEMATICAE IN PHYSICIS UTILITAS. 169 

Quapropter cum in rebus naturalibus demonstratio habetur per 
causam per vias mathematicae, et demonstratio per effectum 
habetur per vias naturales, plus potest mathematicus in rebus 
naturalibus sciendis, quam ipse philosophus naturalis, Et 
maxime hoc planum est, quod motus simpliciter violentus, 
ut motus gravis sursum, generabit calorem, et longe magis 
quam naturalis motus; quia in violenter moto sunt duae 
virtutes motrices omnino contrariae, et secundum totum, et 
in contrarias partes omnino, ut virtus naturalis gravis tendit 
deorsum, et virtus violenta tendit omnino sursum. Et ideo 
m^na est distinctio partium rei motae violenter, et major 
quam in naturali. 



Capitulum XVI. 

De motu Librae. 

Et cum jam dictis expedit altius aperire geometricam Re«earchcs 
potestatem in motibus ; et hoc propter intcUectum univer- on pavtty. 
salem scientiae de ponderibus, quae est pulchra et difficilis 
nimis hominibus non habentibus experientiam causarum in 
motibus gravium et levium. Dicit ergo Jordanus in libro 
de ponderibus\ quod si aequilibris fuerit positio aequalis, 

^ This was Jordanus Nemorarius, the most original, if we except Leonardo 
Fibonacci. of the mathematicians df the thirteenth century. There b good ground 
for believing that he is identical with Jordanus Saxo who, on the death of 
St. Dominic, laai, succeeded to the generabhip of the order. His principal 
works are, {i) De PoneUrilms, of which an edition was published in 1533, by Peter 
Apianus ; (a) a treatise on Arithmetic, edited in Paris» 1496 and 1514, by Faber 
Stapulensis ; (3) Algoriihmua Demonsiratus, edited by SchOner, of Nuremberg, in 
1534 ; (4) -^ Numeris DatiSy printed in Zeitschrift, Math. Phys. zxxvi histor. 
literar. Abtheilung, 1891 ; (5) De Triangulis, printed 18B7, by the Copemicus- 
verein Alr Wissenschaft und Kunst of Thom. Most of these works were 
evidendy known to Bacon. The treatise, De Ponderibus, which consists of 
a short preface foUowed by thirteen propositions, is interesting as one of the 
earliest studies, by a mathematician of great originality, of the mechanics of 
a partide forming part of a rigid system. With regard to gravity we find, of 
course, the doctrine, still awaiting Galileo^s refutation, that heavy bodies faU 
more rapidly than lig^t. The arithmetical treatise, containing many algebraic 
problems, bad also been studied by Bacon, as his fragment on the Prindples of 
Mathematics dearly shows. [Sec Cantor, Gtsek, der Maihem. vol. ii. pp. 49-54-] 



T70 OPERIS MAJORIS PARS QUARTA. 

aequis ponderibus appensis, ab aequalitate non discedet, 
et si ab aequidistantia separatur ad aequalitatis situm 
revertetur. Et istud videmus ad sensum in lance utraque, 
quarum virga sit ex parte utraque aequalis in longitudine 
ct in pondere, et omnino appendantur pondera aequalia, 
et libra aequaliter teneatur per appendiculum, ut stet appen- 
diculum ad angulos rectos super regulam librae in centro 
revolutionis, nam hic punctud vocatur centrum revolutionis 
a quo appendiculum exit ad angulos aequales. Et dicitur 
centrum revolutionis, quia quando per violentiam manus 
deprimentis alterum ponderum aequalium, aut propter in- 
aequalitatem appensorum unum eorum facit nutum, aliud 
elevabitur, et hic motus descensus et elevationis describet 
circulum unum, cujus ille punctus a quo exit appendiculum 
est centrum, et ideo dicitur centrum revolutionis. Quod ut 

planius sit fiat figura. Nam sit 

regula seu baculus librae a b^ et c d 

sit appendiculum, tunc centrum revo- 

lutionis a quo exit appendiculum erit 

dj et in circumferentia istius circuH 

appensa movebuntur, nam illud quod 

descendet describet circulum infer- 

iorem, et illud quod ascendet de- 

scribet circulum superiorem. His 

suppositis, arguitur ^ sic. Cum alterum 

brachiorum librae aequalibus appensis nutum faciat pcr manum 

Gravity of deprimentis, fit, secundum Aristotelem quarto Coeli et Mundi, 

g^^J^^J" gravius, quia grave quanto adquiret magis de loco gravis, 

a baiance tanto magis adquirit de forma gravitatis, ut ipse dicit. Ergo 

their^ quod descendit fit gravius, quantumcunque parum descendat 

position. a situ aequalitatis, et ideo quanto magis descendit, tanto erit 

gravius. Ergo fiet inaequale reliquo appenso et ponderosius 

eo. Ergo licet fuerint in situ aequalitatis aequalia, tamen 

cum recedunt ab illo situ fient inaequalia in pondere ; quare 

semper descendet illud quod nutum facit, et aliud semper 

ascendet, et ideo nunquam ad situm aequalitatis revertentur. 

^ J.'8 reading, argumentor, for arguitur, suggests that what foUows is Bacon's 
opinion : which it is not. 




MATHEMATICAE IN PHYSICIS UTILITAS. 171 

Sicut quando duo pondera inaequalia ponuntur in brachiis, 
statim recedunt a situ aequalitatis, et nunquam ad eundum 
situm revertentur, sed semper descendit quod est ponderosius. 
Ergo similiter hic, quod est contra Jordanum et contra 
sensum. Item Jordanus dicit, quod inter quaelibet gravia est 
velocitatis in descendendo et ponderis eodem ordine sumpta 
proportio, sed istud grave quanto magis descendit, tanto fit 
ponderosius. Ergo tanto velocius descendit. Ergo nunquam 
revertetur per naturam ad situm aequalitatis. Item Jordanus 
dicit, quod minus grave secundum situm est, quod descensum 
alterius sequitur motu e contrario^ id est, quod ascendit 
quando desccndit, et e contra. Sed appensum nutum faci^ns 
est minus grave secundum situm, ut probabo. Quare sequetur 
descensum alterius appensi motu contrario, et ascensum 
similiter. Quapropter secundum quod unum descendit, reli* 
quum ascendit, et e contra : quare nunquam in situ aequalitatis 
quiescent. 

Quod autem appensum faciens nutum sit minus grave se- 
cundum situm, manifestum est per hoc, quod minus capit de 
directo descensu in diametro transeunte per centrum revolutionis 
versus centrum mundi : quapropter secundum Jordanum erit 
minus grave secundum situm. Et hoc exigit ipsa veritas per 
figuram declaranda. Et hujusmodi figuratio solvet objecta, nec 
potest habere remedium intellectus nisi per figuram. Descri- 
batur ergo circulus super centrum revolutionis, quod est o^ in 
cujus circumferentia appensa revolventur, et trahatur diameter 
a b aequidistans horizonti, et lineetur alia diameter intersecans 
hanc quae tendat in centrum mundi, et sit dc, et signentur 
arcus aequales in utroque semicirculo ab utraque parte diametri 
aequidistantis horizonti, et hoc a parte utriusque termini ejus, 
et a terminis arcuum ducantur in utroque semicirculo lineae 
aequidistantes sibi invicem, et diametro aequidistanti hori- 
zonti, quae sunt/A,^/, /^, j r, quae omnes secant diametrum 
cadentem in centrum mundi. Oportet ergo secundum Jor- 
danum et commentatorem ejus, quod illae lineae aequidistantes 
secent de diametro quae vadit in centrum mundi, partes 
inaequales, ita ut illa aequidistans, quae propinquior est 
diametro aequidistanti horizonti, secet majorem partem 



172 



OPERIS MAJORIS PARS QUARTA. 




FlG. 30. 



diametri alterius, quam remotior aequidistans, ut / q separabit 
majorem partem diametri d c quam s r, ita ut pars diametri 

d c, quae est inter « ^ et / ^ sit 
major quam pars ejusdem diametri 
quae est inter / ^ et j r, et eodem 
modo pars diametri d c^ quae est 
inter a b ^X. g p^ erit major quam 
illa quae est inter gp et f h. Et 
secundum hoc oportet quod sumpta 
una aequidistante in semicirculo 
uno^ et alia in alio, quae aequaliter 
distant a diametro eis aequidistante, 
illae secabunt partes aequales de 
diametro descendente in centrum mundi xxt tq ttgp secabunt 
partes aequales de dc^ et similiter s r et/ A, sicut dicit vicesima 
sexta propositio de triangulis Jordani. Si ergo partes diametri 
cadentes in centrum mundi divisae per aequidistantes sunt 
inaequales, ita ut illae partes diametri quae dividuntur per 
aequidistantes propinquiores diametro aequidistanti horizonti 
sint majores ; tunc ergo intelligamus r^ulam librae jacere in 
diametro aequidistante horizonti, et appendiculum sit erectum 
in diametro cadente per centrum, ut libra sit in situ aequalitatis 
et brachia ejus, deinde postea moveatur libra, et elevetur pars 
una librae usque ad primam aequidistantem in semicirculo 
superiori, et alia deprimatur usque ad terminum primae 
aequidistantis in semicirculo inferiori, ut regula sit in situ tp 
lineae, et pars librae altior sit in /, et reliqua in /. Si ergo 
p descendat usque ad terminum alterius aequidistantis h^ 
transibit de diametro cadente in centrum, partem ejus quae 
est inter aequidistantes gP ^tf h, quod minus est quam illa 
pars diametri, quae est inter t q eXa byUt patet ex praedictis, 
Ergo si descenderet usque a caperet plus de descensu recto 
in diametro cadente in centrum mundi quam/,dum descendit 
in h ; quare / est gravius secundum situm quam/. Et iterum 
/ descendit versus centrum mundi. Sed p propter declina- 
tionem circuli recurvatur a centro, et saltem minus tendit in 
centrum, ut patet ad sensum. Ergo relinquitur, quod ex hac 
causa adhuc erit minus grave. Et quia sic est, ideo solvitur 



MATHEMATICAE IN PHYSICIS UTILITAS. 173 




prima objectio; nam licet pars regulae^ / descendens est 

propinquior centro mundi, ut patet, si linea recta trahatur ab 

eo in centrum o^ quia illa Hnea est 

brevior quam Hnea quae trahitur a /, 

ut patet ad sensum, et ita gravior sit 

in quantum plus habet de loco deorsum, 

tamen quia/ secundum illam rectam 

lineam, quae est f o non movetur 

versus centrum, sed secundum circu- 

lationem circumferentiae drculi, et illa 

circulatio facit eam minus capere de 

incessu recto in diametro cadente in 

centrum quam capiat /, atque obliquat 

et incurvat ipsum / a centro, ut non 

ita recte tendat in centrum sicut /, 

quando descendit, oportet quod / sit 

gravior quam p dum sunt in tali 

situ. Et ideo si dimittantur sibi ipsis / descendet, et ejus 

descensum sequetur / motu contrario, scilicet ascendendo 

usque ad situm aequalitatis. Et ideop non semper descendet, 

sed praevalent duae causae g^avitatis hic assignatae contra 

illam de qua objectio fecit mentionem. Iterum illa gravitas 

non cogit, nam modica est et insensibilis, et ideo non operatur 

hic, sicut nec si pluma una apponeretur ad alterum appensorum 

aequalium, cum sunt in situ aequalitatis, faceret nutum, et 

tamen secundum veritatem illud brachium ubi fuerit pluma 

est gravis, quia pluma habet aliquid gravitatis. Et ideo 

similiter est hic ; quia enim brachium descendens, quando est 

in ultimo descensu parum distat a situ aequalitatts, ideo valde 

modicum et insensibile est quod adquirit de gravitate, et ideo 

gravitas acquisita non est computanda. 



FiG. ai. 



^ Jebb's fig^re (Tab. i. 96) is wrong, as he puts p in the upper instead of the 
lower end of the balance. Further, he draws po and o/ to the centre of the 
circle, in which case both are, of course, equal. The lines should be drawn to 
the centre of the earth, as in fig. ai. What is meant is thatp is nearer to the 
earth's centre than /, and therefore moves with greater force : but that this is 
counterbalanced by the fact that the path of p tends to become more horizontal 
ihan thatof /; 'minus capit de incessu recto in diametro cadente in centrum 
quam capiat /.' 



174 OPERIS MAJORIS PARS QUARTA. 

Et tunc patet aliud, quod hujusmodi ponderositatem 
majorem concludit quod semper velocius descendet ut nun- 
quam elevetur. Jam enim patet, quod haec gravitas nihil 
facit sensibile, atque duae causae gravitatis praetactae 
reperiuntur in brachio altiore. Cum vero in tertio argumento 
dicit, quod minus grave est quod descensum alterius sequitur 
motu e contrario, scilicet ascendendo, bene concedo. Nam sic 
se habet appensum inferius, quia movetur sursum, quando 
appensum superius descendit, ut quando sibi ipsis dimittuntur, 
et sunt aequalia, sicut positum est. Sed non propter hoc 
ascendit plus et plus, nec reliquum descendit quantum potest, 
sed solum attingunt situm aequalitatis, et ibi nata sunt 
quiescere, propter quod objectio concludit plus quam deberet, 
quando vult ex hoc, quod unum ascendit et reliquum de- 
scendit, concludere quod transeant situm aequalitatis. 
Oscillation Et si dicatur, quod ibi est motus titubationis et ideo 
daeto brachium superius descendit ultra situm aequalitatis et qua 
atmo- ratione transit parum et multum, quia hic transitus est unius 
naturae, et similiter de reliquo brachio ut ascendat semper, 
postquam transit situm aequalitatis. Sed dicendum est, quod 
hic descensus brachii altioris ultra situm aequalitatis non est 
propter naturam ipsius appensi, sed propter reinclinationes 
partium aeris impetuosas. Cum enim ^r rcceperit motum, 
retinet ipsum bene, et ideo diu titubant partes ejus huc atque 
illuc, et non permittunt statim appensum quiescere in loco 
aequalitatis K 

* The remaining portion of Part IV is not divided into chapters, with the 
exception of the final section on astrology, which in the Bodleian MS. is divided 
as though it were a distinct treatise. What foUows consists first of a disquisi- 
tion on Chronology, secondly, of a review of geographical knowledge, and 
thirdly, of the treatise referred to. 

In the Opus Tertiumj before those subjects are entered upon, therc occur some 
discussions of matters not treated of in the Opus Majus ^chapters 42-52). lliese 
deal (a) with the question of Vacuum : (6) following on this, with the question 
of growth and nutrition : (c) of place and motion with regard to immaterial 
beings : (</) of etevum^ or created eternity. 



MATHEMATJCAE IN DIVINIS UTILITAS. 175 



MATHEMATICAE IN DIVINIS UTILITAS. 

Postquam ' manifesta est necessitas mathematicae in rcbus Connexion 
hujus mundi et in scientiis humanis nunc potest istud idem maticswith 
ostendi in divinis. Et hoc est magis considerandum, quia ^**^^®gy- 
humana nihil valent nisi applicentur ad divina. Cum igitur 
ostensum sit quod philosophia non potest sciri nisi sciatur 
mathematica, et omnes sciant quod theologia non potest sciri 
nisi sciatur philosophia, necesse est ut theologus sciat mathe- 
maticam. Caeterum Deus posuit res creatas in scriptura sua, 
qui solus novit potestatem creaturarum quas condidit, nec 
potest falsum sentire, nec decet suam veritatem. Ergo cum 
omnes res a Deo et angeh's et summis coelorum usque ad 
terminos eorum ponantur in scriptura, vel in se vel in suis 
similibus vel in suis contrariis, et contrariorum est eadem 
scientia, ut dicit Aristoteles, et verum est vel in universali 
vel in particulari, necesse est theologum scire res hujus mundi, 
si textum sacrum debet scire. 

Praeterea nos videmus, quod sensus literalis stat in cogni- 
tione naturarum et proprietatum creaturarum, ut per con- 
venientes aptationes et similitudines eliciantur sensusspirituales. 
Nam sic exponunt sancti et omnes sapientes antiqui, et haec 
est vera et sincera expositio, quam Spiritus Sanctus docuit. 
Quapropter oportet theologum scire optime creaturas. Sed 
ostensum est, quod sine mathematica sciri non possunt. 
Ergo mathematica omnino est necessaria sacrae scientiae. 

Et hoc tertio per propria potest ostendi. Et cum multis Mathe- 

modis probabitur quod intendo, primo tamen per occupationes Sowledge 

sanctorum persuadere conabor, cum exclusione infamiae ^^ , ^ 

patnarchs. 
mathematicae quam multi imprudenter allegant, quia sanc- 

torum testimonia non intelligunt. Patriarchae enim et 

Prophetae ante diluvium et post invenerunt ipsam et docuerunt 

caeteros homines, i. Chaldaeos, 2. Aegyptios ; et ab Aegyptiis 

ad Graecos descendit; et non ita evidenter scribitur quod 

^ Cf. Opus TerHum, chap. 54. 



176 OPERIS MAJORIS PARS QUARTA. 

sic laboraverunt in aliis scientiis. Sed cum per istos viros 
data est nobis lex divina, et fuerunt sanctissimi, non occupa- 
verunt se nisi in scientia quae maxime est utilis I^i divinae ; 
ergo mathematica est maxime consona legi divinae. Minor 
propositio habet secum suam probationem. Major probatur 
per auctoritatem triph'cem. Primo per historic^raphos, et 
praecipue per maximum eorum Josephum. Primo enim 
Antiquitatum libro in tribus locis de his scientiis faciens 
mentionem, expresse narrat totum quod propositio major 
proponiL Nam dicit, * quod filii Adae invenerunt geometriam, 
astronomiam, arithmeticam, et musicam ; et Noe et filii ejus 
docuerunt Chaldaeos: deinde Abraham docuit Aegyptios.' 
Apprecia- 1 Secundo, verificatur hoc per beatum Hieronymum et 
the fathers. Cassiodorum et alios doctores sacros, ut vulgus etiam theo- 
logorum non ignorat; et ratificant sancti, quod Josephus 
asseverat. Tertio, per philosophorum assertionem. Quoniam 
Albumazar quinto libro majoris introductorii in astronomiam 
undecima doctrina sive undecimo capitulo refert Sem filium 
Noe hujus scientiam alios docuisse, atque in prologo composi- 
tionis astrolabii Ptolemaei dicitur, quod a filio Sem, qui divina 
memoria commonitus erat, aut fortasse divino nutu commotus, 
hujus scientiae studium in orbem derivatum affirmatur. Hoc 
idem indicat sanctorum nostrorum post adventum Domini 
occupatio, ut Augustini, Cassiodori, Isidori, Hieronymi, Orosii, 
Bedae, Origenis, Eusebii Caesariensis. De his enim scripserunt, 
et in his se et alios exercitaverunt solum, aut magis quam in 
aliis. Cum ergo isti fuerunt doctores sacrae scripturae et 
viri sancti, manifestum est, quod hujusmodi scientiae maxime 
valent sacrae scientiae professoribus. Quod autem ipsi de his 
scripserunt, manifestum est per Cassiodorum et Isidorum, qui 

' This passage is much abbreviated in O. Thus : ' Secundo verificatur per 
doctores sanctos quos recitant sancti : quod Josephus asseverat. Quod autem, 
de his scripserunt manifestum est per Cassiodorum et Isidorum quum tractatus 
suos de omnibus istis quatuor composuerunt. Augustinus etiam de numeris et 
musica libros diversos conscripsit. Sed non solum isti sed alii multi. £t 
Cassiodorus dicit, Mathematica dicere valeamus quaecunque docentur, hoc 
tamen signum commune propter sui excellentiam proprie vindicavit. £t in 
tractatu,' &c. O. has many other omissions in this section of the work, which 
arc supplied by the two Cottonian MSS., Tib. C. v, and JuL D. v. I have 
indicated some of them, but not all. 



MATHEMATICAE IN DIVINIS UTILITAS. 177 

tractatus suos de omnibus istis quatuor composuerunt. 
Augustinus etiam de numeris et musica libros diversos 
conscripsit ; Hieronymus in libris diversis, et Orosius ad 
Augustinum« et Eusebius de mundi locis, quorum certificatio 
eruitur ex fontibus astronomiae, sicut certum est, et sequentia 
declarabunt. Beda de cursu solis et lunae, et de tota temporis 
diversitate, atque Origenes et Eusebius, quae astronomiae 
subjacere noscuntur. Non solum vero de his scripserunt, sed 
et idoneos docuerunt haec, ut essent acuti contra haereticos, 
sicut patet per Cassiodorum in mathematica sexto libro Eccle- 
siasticae Historiae; etiam partes geometriae et arithmeticae 
disciplinae, ut ibidem dicitur, quae magis a divinis elongantur 
quam astronomica et musicalia. Sed non tantum occupaverunt 
se scribendo et alios docendo, imo veritates theologicas per 
virtutem harum scientiarum exposuerunt ; sicut per omnia 
originalia sanctorum sine contradictione manifestum est, ut 
evidenter patet in numeris et locis mundi et rebus coelestibus 
et aliis quae ad dictas scientias pertinere noscuntur, sicut 
patebit inferius. 

Sed non solum sic exposuerunt sacra de facto, scd verbo 
asserunt has scientias per omnem modum valere rebus divinis, 
et super alias scientias extoUunt in hac parte. Cassiodorus Cassio- 
quidem in praefatione de artibus et disciplinis secularium °™* 
studiorum sic ait, * Mathematicam Latino sermone Doctrinalem 
possumus appellare, quo nomine licet omnia doctrinalia dicere 
valeamus quaecunque docentur, haec tamen sibi commune 
vocabulum propter sui excellentiam proprie vindicavit' Et in 
tractatu mathematicae sic ait, * Disciplinales sunt, quae 
nunquam opinionibus deceptae fallunt, et ideo tali nomine 
nuncupantur. Has dum frequenti meditatione revolvimus, 
sensum nostrum acuunt» limumque ignorantiae detegunt, et 
ad illam speculativam contemplationem, Domino largiente, 
perducunt ; quas merito sancti patres legendas persuadent, 
quoniam ex magna parte per eas a carnalibus rebus appetitus 
abstrahitur, et faciunt desiderare, quae solo Domino largiente 
corde possumus respicere. Duplex quidem pars mathematicae 
tam a sanctis quam a philosophis ipsis numeris attribuitur 
vulgato sermone, videlicet arithmetica de numeris absolute, et 

VOL. I. N 



178 OPERIS MAJORJS PARS QUARTA. 

musica de proportionibus et rationibus caeteris quae in 
numeris reperiuntur, prout ad sonum et gestum referuntur ; 
quia sonus et gestus sunt praecisum musicae subjectum, dis- 
cussi tamen per proportiones numerorum in musicae scientia.' 
Augustine*s Augustinus autem in secundo de Ordine Disciplinae dicit) 

view of , , ,. . . . . , , 

arithmetic, ^d divinarum scnpturarum nemmem aspirare debere sme 
scientia potentiae numerorum.* Atque in secundode Doctrina 
Christiana dicit, * numerorum imperitia multa facit non intelligi 
translate et mystice posita in scripturis'; et ponit exempla 
plurima, adjungens, * quod ita in aliis multis numerorum formis 
secreta in sanctis libris ponuntur, quae propter numerorum 
imperitiam legentibus clausa sunt' Et ideopropter utilitatem 
numerorum maximam Isidorus * in tractatu arithmeticae dicit, 

* Adime seculo computum, et cuncta ignorantia caetera com- 
plectitur; nec differre possunt a caeteris animalibus, quae 
calculi nesciunt rationem.' 

ofmuBic, Quamvis autem jam communiter cum arithmetica patet 
laus musicae, propter hoc quod utraque proportiones quae in 
numeris sunt considerat, tamen numeros, ut sunt in sonis, 
maxime laudat Augustinus ad Omerium dicens, ' In omni- 
bus rerum motibus quid valeant numeri facilius consideratur 
in vocibus, eaque consideratio quibusdam gradatis itineribus 
nititur ad superna itinera veritatis, in quibus viis se ostendit 
sapientia hilariter.' Et in libro Retractationum dicit*, 

* Sextus maxime innotuit, quoniam in eo res digna cognitione 

* Bom in Carthagena, 570. In 601 he became bishop of Seville, succeeding 
his brother Leander, the 'apostle of Spain/ and held the bishopric till his death 
in 636. His great powcrs were principally devoted to organizing the work of 
the Church in Spain. But he was a man of wide leaming. and is placed by 
Dante {ParadisOj x) in the Sphere of the Sun with Albert, Thomas Aquinas, and 
other great theologians. His principal work is a Cyclopaedia, founded on the 
works of Martianus Capella and Cassiodorus, entitled Ortgints, in twenty books, 
from which much is to be gathered as to the very limited scientific knowledge 
of Christendom in the seventh century. The passage here quoted is in lib. iii. 
cap. 4. (Cf. Cantor, vol. i. pp. 705-7.) This work continued to be of g^eat 
authority throughout the middle ages. 

' O. has, ' Maxime pervenitur a mutabilibus rebus ad immutabiles ac si Dei 
invisibilia per ea quae facta sunt conspiciantur. £t in hbro de Doctrina Chris* 
tiana posuit exempla de psalterio decachordo, et admittit quod musicam in 
pluribus locis et in sanctis scripturis honorabiliter positam invenimus. Cassio- 
dorus in tractatu musicae sic ait, Musica disciplina,' &c 



MATHEMATICAE IN DIVINIS UTILITAS. 179 

versatur, quomodo a mutabilibus numeris perveniatur ad 
immutabiles, ac si invisibilia Dei per ea quae facta sunt 
conspiciantur/ Item in libro de Doctrina Christiana dicit, 
'Non pauca claudit atque obtegit in sanctis libris rerum 
musicarum ignorantia/ et ponit exempla in psalterio decachordo 
et cythara et hujusmodi, et adjungit, * quod musicam in 
plerisque locis in sacris scripturis honorabiliter positam 
invenimus/ Cassiodorus quidem et in mandatis Dei et moribus 
et scriptura sacra et in omnibus rebus creatis eam valere 
dijudicat. Unde in tractatu musicae sic ait, * Musica disciplina 
per omnes actus vitae nostrae diffunditur ; primum si creatoris 
mandata faciamus, et puris mentibus statutis ab eo regulis 
serviamus, musica quippe est scientia bene modulandi. Quod 
si nos vitam bona conversatione tractamus tali disciplinae 
probamur semper esse sociati. Quando vero iniquitatem 
gerimus, musicam non habemus. In ipsa quoque religione 
valde permixta est; unde decalogi decachordus^ tinnitus 
cytharae, tympana, organi melodia, cymbalarum sonus ; ipsum 
quoque Psalterium ad instar instrumenti musici nominatum non 
dubium est, eo quod in ipso contineatur virtutum coelestium 
suavis nimis et grata modulatio ; et ut breviter cuncta com- 
plectar, quicquid in supernis sive in terrenis rebus convenienter 
secundum actoris sui dispositionem geritur, ab hac disciplina 
non refertur exceptum. Gratissima vero nimis utilisque 
cognitio, quae sensum nostrum ad superna erigit et aures 
modulatione permulcet.' 

De utilitate et scientia astronomicorum dicit, * Astronomiam of astro- 
si casta et moderata mente perquirimus, sensus nostros, ut ^^^^* 
veteres dicunt, magna claritate perfundit. Quale enim est 
ad coelos animam subjicere * et totam illam machinam super- 
nam indagabili ratione discutere, et inspective mentis subtilitate 
ex aliqua parte colligere, quod tantae magnitudinis arcana 
velaverunt' Et subjungit, * Ex quibus, ut mihi videtur, 
climata nosse, horarum spatia comprehendere, lunae cursum 
pro inquisitione Paschali, ne simplices aliqua confusione tur- 
bentur, qua ratione fiat advertere, non videtur absurdum. 
Est et alia quoque de talibus non despicienda commoditas, si 

^ Caelos animo subire, J. 

N % 



i8o OPERIS MAJORIS PARS QUARTA. 

opportunitatem navigationis, si tempus arandi, si acstatis 
caniculam, si autumni suspectas imbres inde discamus/ Et 
Augustinus in libro secundo de Doctrina Christiana de utilita- 
tibus istius scientiae loquens, vult triplicem utilitatem ejus 
esse, videlicet, * demonstrationem praesentium, et cognitionem 
praeteritorum, et rationabiles conjecturas futurorum. De- 
monstratio praesentium in assignatione proprietatum rerum 
coelestium consistit. Et praeter demonstrationem praesentium 
habet praeteritorum narrationi simile aliquid, eo quod a prae- 
senti cognitione motuque siderum in praeterita eorum vestigia 
regulariter licet recurrere. Habet etiam regulares conjecturas 
futurorum non suspiciosas et ominosas, sed ratas et certas,' 
of geo- ut ait. Et cum sic sentiant sancti de tribus partibus posteri- 
»nco- oribus mathematicae, necesse est eos de parte prima lauda- 
biliter sentire, quae scilicet est geometria. Ex hujus enim 
notitia caeterae dependent, cum prima sit omnium et radix 
caeterarum. De cujus laude scribens Cassiodorus sic dicit, 
* Etenim si fas est dicere, sancta divinitas^ quando creaturae 
suae diversas species formulasque dederit, quando cursus 
stellarum potentia veneranda distribuit et statutis lineis facit 
currere quae moventur, certaque sede quae sunt fixa constituit, 
quicquid bene disponitur ac completur, potest disciplinae hujus 
qualitatibus applicari/ 
Sevcn Et si velimus descendere ad propria studii theologiae in- 

rcspects m . _ . . . 

which veniemus mathematicam omnino necessariam propter septem 
maiira are "^^S"*^ causas. Una est notitia coelestium rerum ; nihil enim 
ofuscto est ita conveniens theologiae et ejus professoribus. Nam 
(,^K*now- theologia est coelestis divinitus ; et ideo nuUa scientia humana 
ledgeof the speculativa conveniet ei in tantum sicut coelestis. Et per 

hcaveos. . . . , , . . 

totam scnpturam a terrenis revocamur et ad coelestia excita- 
mur. Et conversatio nostra secundum Apostolum in coelis 
est si sumus vere Christiani, atque aspiramus et credimus nos 
fore mansuros corporaliter in coelo et perpetue. Quapropter 
nihil deberet tantum sciri a nobis sicut coelum, nec aliquid in 
humanis tantum desiderari. Et si nos gaudemus exponere 
scripturam, justum est exponi per rerum inferiorum proprie- 
tates quae in scriptura ponuntur et aliter sciri non possunt. 
Quare similiter cum in scriptura sint multa de coelestibus et 



MATHEMATICAE IN DIP7NIS UTILITAS. i8i 

difiicilia, necesse est theologum scire coelestia. Praeterea 
cum rerum magnitudo excitet nos ad reverentiam creatoris, 
et non est comparatio rerum inferiorum ad coelestium magni- 
tudincm, tunc cognitio inferiorum non habebit comparationem 
superiorum respectu finis, qui est laus et reverentia creatoris. 
Dicit enim Avicenna in nono Metaphysicae, * quod ea quae sunt 
sub circulo lunac sunt pene nihil comparatione eorum, quae 
sunt supra/ Et Ptolemaeus ostendit in Almagesto et omnes 
sciunt astronomi, quod tota terra cum omnibus inferioribus se 
habet respectu coeli sicut centrum ad circumferentiam. Sed 
centrum non habet aliquam quantitatem. Quapropter con- 
similiter concludunt de terra respectu coeli, licet in se sit 
magnae quantitatis. Et minima stellarum visu notabilium, ut 
dicit Alfraganus in principio sui libri, est major terra ; sed 
minima stellarum respectu coeli non habet quantitatem, de 
qua sit vis. Et cum ex octavo Almagesti et ex Alfragano 
pateant sex stellanim fixarum magnitudines, quaelibet illarum 
quae sunt in prima magnitudine, est aequalis terrae circiter 
centies et septies. £t illarum quaeh'bet quae sunt in sexta mag- 
nitudine, est aequalis terrae decies octies. Et sol est centies 
septuagies fere major tota terra, sicut probat Ptolemaeus 
quinto Almagesti. Et secundum eum una stella non complet 
motum suum semel in circuttu coeli nisi in triginta sex millibus 
annorum propter coeli magnitudineni, cum tamen stella movea- 
tur incredibili velocitate. Sed terra tota posset perambulari 
infra tres annos. Quapropter magnitudo inferiorum non habet 
comparationem ad coelestia. Similiter nec utilitas ; quia tota 
utilitas inferiorum causatur ex superioribus. Duplex enim 
allatio solis sub obliquo circulo cum aspectibus planetarum 
est causa omnium quae fiunt hic inferius. 

Si ^itur descendamus ad coelestia secundum considera* 
tiones theolc^iae, patet quod theologi quaerunt in sententiis 
et tractatibus super sententias, an orbes coelestes sint con- 
tinui vel discontinui, et de numero coelorum, maxime propter 
nonum et decimum, et de figura eorum et circulis epicyclis 
et eccentricis, et motibus in illis, et de differentiis positionuni 
in coelis, ut de dextro et sinistro, ante et retro, et sursum 
et deorsum, et de proprietatibus codorum, ut de luce et 



i82 OPERIS MAJORIS PARS QUARTA, 

perspicuo et hujusmodi, atque de influentia coelorum ia 
haec inferiora, et de differentia coeli et naturae elementaris 
praecipue propter ignem. Nam Augustinus et alii aliquando 
secundum opinionem Platonis nominant coelum esse igneae 
naturae. Quaerunt etiam de locis mundi propter paradisum, 
an sit sub aequinoctiali circulo vel non ; et de infemo ubi 
sit ; et utrum coelestia habent posse super generabilia et 
corruptibilia, et utrum super animam rationalem ; et de fato 
et hujusmodi quae ad judicia astronomiae noscuntur pertinere ; 
et alia innumerabilia multiplicantur quotidie in quaestionibus 
theologiae. Sed non solum tractatus sententiarum, sed 
ipse textus sacer cum expositionibus sanctorum hoc requirit. 
Nam capitulum primum Genesis multas habet difficultates 
propter coelestia, ut ex ipso textu patet, et per expositiones 
sanctorum, praecipue Basilii, Ambrosii, Bedae, in libris suis 
qui Exemeron vocantur. Et in Josue, propter diei longitu- 
dinem, sole stante, praecipue per operationem ad longitudinem 
diei, qua retrocessit sol decem lineis ad verbum Isaiae pro- 
phetae. Nam videtur esse contradictio in his locis. Atque 
cum Salomon dicat in Ecclesiaste quod sol omni die secundum 
expositionem Hieronymi in originali flectitur ad aquilonem, 
vix aliquis mathematicorum potest hoc inteUigere. Quoniam 
sciunt quod a solstitio hyemali usque ad solstitium aestivale 
flectatur omni die ad aquilonem per gradum unum fere. Sed 
in alia medietate anni e converso. Et de altitudine firma- 
menti in Ecclesiastico ; et quomodo sol in meridiano exurit 
terram, ut ibidem dicitur^ indigent astronomica capacitate. 
Atque Hyades et Pleiades et Arcturus atque Orion, et interiora 
Austri de quibus beatus Job loquitur, habent magnam diffi- 
cultatem, praecipue cum dictat beatus Hieronymus super 
Isaiam, quod Orion habet xxii stellas, quarum novem primae 
sunt in tertia magnitudine, et novem aliae in quarta magni- 
tudine, et quatuor residuae in quinta magnitudine, nec plus 
dicit. Sed haec sciri non possunt nisi ex octavo Almagesti, 
ubi sex gradus magnitudinis stellarum assig^antur, et de- 
terminantur quae stellae sunt in qualibet illarum. Et quia 
infinita sunt alia in scriptura et in expositionibus sanctorum, 
quae scientiam coelorum et astronomiae judicia tangunt : 



MATHEMATICAE IN DIVINIS UTILITAS. 183 

quapropter necesse est theologum bene scire coelestia, tum 
propter occupationem quaestionum in sententiis et summis, 
tum propter ipsum textum. 

Secunda radix astronomiae respectu theologiae et proprie (a) Astro- 
respectu textus consistit in locorum mundi consideratione. °e™(J^ 
Nam totus textus est plenus his locis, et ideo nihil magnificum Bibiicai 
sciri potest nisi sciantur haec loca. Tota enim series scripturae 
decurrit penes regiones, civitates, deserta, montes, maria, et 
caetera loca mundi, quorum certitudo non potest haberi nisi 
per scientias praedictas, quia harum proprium est distinguere 
partes habitabiles a non habitabilibus, et habitabile dividere 
in tres partes magnas, Europam, Africam, et Asiam, et istas 
tres in septem climata nota, praeter alia climata irregularia 
quamplura. £t haec climata certitudinaliter nisi per virtutem 
illarum scientiarum nescit quisquam separare in provincias et 
r^iones et caetera loca, ut inveniantur civitates notae et 
famosae, sicut Jerusalem, Babylon, Meroe, Alexandria, Anti- 
ochia, Ephesus, Athenae, Tarsus, Roma, et caeterae prae aliis 
notatae ab astrologis secundum debitam distantiam ab invicem, 
et ab oriente et ab occidente, septentrione et meridie, quibus 
inventis poterunt et regiones famosae ab eis denominatae 
inveniri, et maria et deserta et montes et omnia quae in sacris 
literis continentur. Hic enim est magna utilitas istarum 
scientiarum in sacra scriptura. Et forte nihil utilius de philo- 
sophia poterit inveniri ; quoniam qui ignorat loca mundi, ei 
multoties non sapit cortex historiae per loca infinita, et 
maxime propter falsitatem multiplicem bibliarum novarum; 
atque per consequens ad intellectus spirituales impedietur 
ascendere et non nisi imperfecte poterit eos explicare. Qui 
vero imaginationem bonam locorum habuerit, et situm eorum 
et distantiam et altitudinem et longitudinem latitudinem et 
profundum cognoverit, necnon et diversitatem eorum in calidi- 
tate et siccitate, frigiditate et humiditate, colore, sapore, odore, 
et pulchritudine, turpitudine, amoenitate, fertilitate, sterih*tate, 
et aliis conditionibus expertus fuerit, et optime placebit ei 
historia literalis, et de facili atque magnifice poterit ingredi ad 
intelligentiam sensuum spiritualium. Non enim est dubium 
quin viae corporales significent vias spirituales, et loca corpo- 



184 OPERIS MAJORIS PARS QUARTA. 

ralia sigtiificent terminos viarum spiritualium et convenientiam 
locorum spiritualium, quoniam locus habet proprietatem 
terminandi motum localem et rationem continentiae ; et ideo 
istorum locorum cognitio et literam facit, ut dictum est, 
intelligi, et vias parat ad intelligentias spirituales : quod multi- 
pliciter confirmatur per dicta et facta et scripta sanctorum. 

Primo, quia dicit Hieronymus in prologo secundi Parali- 
pomenon, ' Sanctam scripturam lucidius intuebitur, qui Judaeam 
oculis contemplatus est, et antiquarum urbium memorias, 
locorumque vel eadem vocabula vel mutata cognoverit.' 
Secundo, quia laboraverunt sancti in videndo loca illa et 
circumeundo. Propter quod beatus Hieronymus dicit prae- 
dicto prologo, * Nobis curae fuit cum eruditissimis Hebrae- 
orum hunc laborem subire, ut circumiremus provinciam, quam 
universae Christi Ecclesiae sonant.' Hoc autem non fecisset, 
nisi propter sacrarum literarum intelligentiam. Tertio, quia 
libros multos scripsit de locis mundi, distantiam et situm 
eorum et caeteras conditiones magna certitudine determinans. 
Orosius etiam ad Augustinum haec loca mirabili utilitate ac 
sincera veritate explicat evidenter. Isidorus autem in pluribus 
locis regiones et civitates utilius, si potest dici, quam priores 
determinat. Cassiodorus autem in climata distinguere non 
omittit. Eusebius etiam Caesariensis, ut narrat Hieronymus 
in libro de locis, post chirographiam terrae Judaeae et 
distinctas tribuum sortes ipsius quoque Jerusalem templique 
in ea cum brevissima expositione picturam ad extremum 
laboravit, ut congregaret nobis de sacra scriptura omnium 
pene urbium, montium, iluminum, viculorum, et diversorum 
locorum vocabula^ quae vel eadem manent vel immutata vel 
aliqua ex parte corrupta. Origenes quidem Adamantius supcr 
Josuam in originali, sicut et in glossa super xviii Josuae 
recitatur, loquens de multitudine locorum in scriptura posito- 
rum, et inter caetcras laudes locorum istorum, sic nos alloqui- 
tur, dicens, *Ne cum fastidio haec legatis, et putetis vilem 
scripturam ex multis nominibus contextam ; sed scitote in 
his contineri majora mysteria quam potest humanus sermo 
proferre, vel auditus mortalis audire.' Cum ergo nostri sancti 
expositores et doctores sacri in istis locis tantum laboraverunt, 



MATHEMATICAE IN DIVINIS UTILITAS. 185 

et tanta mysteria contineri fatentur, non est dubium quin 
eorum cognitio per omnem modum sacrae scripturae est 
necessaria. Sed proprium est astrologiae et astronomiae dare 
rationes locorum mundi et plenam certitudinem. Quapropter 
istae scientiae sunt valde necessariae in hac parte. Possunt 
autem pulchre verificari in exemplis. Qui enim audit historias 
versantes circa Jordanem, Jericho cum planitie sua, montem 
Oliveti, vallem Josaphat, Jerusalem, et non habet imagina- 
tionem locorum istorum et proprietatem eorum, sensum litera- 
lem ignorabit, et ei non immerito non multum sapiet cursus 
historiae, atque per consequens sensus spirituales obteguntur. 
Qui vero scit longitudines, latitudines, profunditates, altitudines, 
varietatem qualitatum, ut calidi, frigidi, sicci et humidi, necnon 
et eoriim quae consequuntur ad haec quatuor, ut moUis, duri, 
grossi, subtilis, asperi, laevis, aridi, liquidi, lubrici, et aliorum 
innumerabilium, quae quarto Meteorologicorum determinan- 
tur; necnon et colores, et sapores, odores, pulchritudines, 
turpitudines, amoenitates, sterilitatem, fertilitatem, naturam 
infectivam, corruptivam, et eis contrarias, et caetera quae in 
locis considerari habent, potest sensum literalem ad purum 
concipere et in eo delectari, atque ad sensus spirituales gloriose 
et placide transire. 

Paucas enim conditiones locorum praedictorum consider- The 
ando, possumus magnificos sensus exprimere moraliter et alle- mdlining of 
gorice et anagogice. Jordanis quidem decurrit ab aquilone Biblical 
ad austrum, et jacet in oriente respectu Jerusalem, quae ^^^*^ ^* 
est in occidente non longe a mari magno posita, et inter 
illa duo primo a parte Jordanis est Jeiicho civitas cum sua 
planitie, deinde mons Oliveti, tertio vallis Josaphat, et tunc 
sequitur Jerusalem. Mundus autem, dicunt sancti, significatur 
per Jordanem secundum rationem interpretationis ejus et 
propter ipsius proprietates, quia currit in mare mortuum, quod 
est instar inferni, et propter multa alia. Et Jericho carnem 
significat, ut volunt sancti. Mons Oliveti significat excel- 
lentiam vitae spiritualis propter montis excellentiam, et 
dulcedinem devotionis propter Oliveti rationem. Vallis 
Josaphat significat humilitatem propter rationem vallis, et 
viam coram oculis majestatis, propter hoc quod interpretatio 



i86 OPERJS MAJORIS PARS QUARTA. 

hujus nominis Josaphat est, in conspectu Domini. Et Jenisalem 
signiiicat visionem pacis, et moraliter est anima sancta quae 
habet paccm cordis ; allegorice significat Ecclesiam militan- 
tem ; anagogice Ecclesiam triumphantem. 

Qui igitur a principio vitae suae seu ab ortu nativitatis suae ab 
oriente rationis deliberantis seu usu rationis vult devenire saltem 
in occidente vitae suae et in senectute ad pacem cordis, et hoc 
moraliter ; et ut sit membrum fidele et perfectum Ecclesiae, 
sub cujus umbra jaceat in pace contra insultus hostis maligni, 
et hoc allegorice ; et ut sit ejus conversatio in coelesti Jeru- 
salem in hac vita, et transferatur in morte ad illam civitatem 
sanctam, ubi sedebit in pulchritudine pacis in tabernaculis 
fiduciae vel requie opulenta ; debet primo Jordanem, id est, 
mundum, aut sibi subjiciendo relinquere, ut sancti seculares, 
aut omnino renunciando recedere, ut religiosi. Ibi enim est 
primus gradus vitae spiritualis et aliis facilior. Quo facto, 
oportet aggredi carnem, quia ipsam non est ita facile vincere 
sicut mundum. Est enim pestis familiaris et non relinquens 
subjectum. Debet autem ipsam non destruere et cum impetu 
frangere, sed paulatim et discrete ejus superbiam domare. 
Propter quod consideratur Jericho cum sua planitie ; et ideo 
debet poenitens plana via procedere, ut rationabile sit ejus 
obsequium, ne si carnem stulte obruat, non possit spiritus ad 
altiora pertingere. Hoc enim est contra multos ad poeni- 
tentiam conversos, qui primo ai\no vel secundo corpora sua 
destruunt, et postea fiunt inutiles, ut nec se nec alios valeant 
juvare. Postquam vero homo mundum subjugaverit, et 
carnem ut oportet domuerit, tunc et non ante est aptus ut 
ascendat ad excellentiam vitae spiritualis et dulcedinem 
devotionis. Ex tunc enim potest ascendere ad montem 
Oliveti et ad cacumen perfectionis attingere, atque in suavitatem 
orationis et contemplationis se immergere. Cum vero fuerit 
sufficienter exercitatus in ascensu et circuitu istius celsitudinis, 
adhuc ^ oportet vallem Josaphat transire, hoc est, totam vitam 
suam in perfecta humilitate debet concludere, ut sit pauper et 
humilis spiritu in conspectu Dei, non in oculis suis vel homi- 
num. Multi enim apparent humiles sibi et aliis, et sunt coram 

^ J. has, < tunc esset in Jenisalem nisi quod oportet.' 



MATHEMATICAE IN DIVINIS UTILITAS. 187 

Deo et angelis superbissimi. Quando vero totam compleverit 
vitam perfecta humilitate, tunc est in Jerusalem, secundum 
ejus sensum triplicem. Habebit enim pacem cordis, quia pax 
talis sequitur vitae spiritualis perfectionem. 'Non enim est 
pax impiis/ dicit Dominus. Sed sancti^ est pax Dei, quae 
exsuperat omnem sensum, et in pace Ecclesiae militantis 
quiescit securus, qua pace carent infideles et peccatores in 
statu damnationis existentes, quos agitat diabolus et turbat de 
peccato in peccatum, et de poena peccati ad novam poenam. 
Et ^ ut dictum est, participabit etiam in hac vita in spe certa 
et revelationibus illa beata visione pacis supernae Jerusalem, 
quam per gratiam Dei in morte consequetur. 

Non solum autem haec loca inter Jordanem et Jerusalem 
cognita et historiam declarant et sensus spirituales explicant, 
sed alia loca innumerabilia quae inter duos hos terminos reperi- 
untur in scriptura. Si quis etiam velit ulterius considerare 
alias conditiones enumeratas, multo magis et quasi incompara- 
biliter poterit sensus divinos elicere, ut patet intuenti. Sed 
modo sufficit innuere quomodo ex paucis multa ex parvis mag^a 
ex planioribus obscura contingat elicere. Sed non possunt loca 
mundi sciri, nisi per astronomiam ; quoniam oportet nos primo 
scire longitudines et latitudines locorum. Latitudo est ab 
aequinoctiali, et longitudo ab oriente, quatenus sciamus sub 
quibus stellis quae loca coaptentur, et quantum sunt a via 
solis. Nam secundum haec videmus sensibiliter res hujus 
mundi variari, et non solum in naturalibus, sed in moralibus. 
Oportet etiam per astronomiam scire, qui planetae dominentur 
quibus r^ionibus; nam secundum hoc potenter immutantur 
regiones. Et multa hujusmodi consideranda sunt per astrono- 
miam, ut sciamus naturas locorum in scriptura ; et non solum 
proptcr loca, sed propter res in eis locatas. Et rerum omnium 
cognitio est necessaria, tam propter sensum spiritualem, quam 
literalem, ut patet ex dictis. 

Tertia radix est de temporibus. Totus enim cursus scrip- (3) Astro- 
turae currit per tempora et secula et aetates a principio mundi v^Tffei 



. nom^ 
verifiei 

usque ad Christum Dominum, et omnia sunt ordinata propter chrono 



^ This and Uie following sentence are omitted in O. 



i88 OPERIS MAJORIS PARS QUARTA. 

ipsum, ut alius legislator non cxpectetur, sed quod ille solus 
sit salvator mundi per suam legem ; quatenus error Judaeorum 
evacuetur de expectatione Messiae ; et error Saracenorum de 
Mahometo qui secutus est Christum ; et error eorum qui 
adhaerebunt adhuc legis latori nefariae qui venturus est, ut 
Albumazar docet libro Conjunctionum, qui in veritate erit 
Antichristus * ; quatenus etiam omnes sectae paganorum, idolo- 
latrarum, Tartarorum, haereticorum, et caeterorum infidelium, 
qui per mundum dispersi sunt per sectas pene innumerabiles, 
deleantur per certificationem temporis' salvatoris, ut nec ante 
eum nec post aliquis alius teneatur, per quem salus humani 
generis habeatur. Sed nuUus potest certificare de temporibus, 
nisi astronomus^ nec aliqua scientia habet de his certificare 
nisi astronomia. Omnes enim mendicant reliquias ejus in hac 
RecUiction parte, ut manifestum est. Et si consideremus inveniemus 
Catendars iwultis modis quomodo astronomia est hic necessaria. Nam 
toChristUn tempora ista, quaedam sunt lunaria, quaedam solaria et lunaria, 
quaedam habent principium determinatum, ut apud Judaeos 
astronomos. Incipiunt enim a lunatione Octobris annum, quia 
sunt usi ab antiquo tabulis et canonibus ad occasum solis 
civitatis Jerusalem. Sed adhuc gaudent uti eis propter terram 
quae data fuit eis a Deo. Quaedam vero habent principium 
indeterminatum, ut tempora solemnitatum apud Hebraeos, et 
tempora Arabum, et hoc diflferenter multum. Quaedam vero 
tempora sunt solaria, et horum quaedam semper habuerunt 
quartum ultra dies integros, ut tempus Graecorum et Latino- 
rum ; quaedam nunquam, ut tempora Persarum ; quaedam 
aliquando sic aliquando non, ut tempora Aegyptiorum. Et 
principia annorum variantur apud ipsos, sicut canones astro- 
nomiae docent et Almagesti, et alia multa. Cum igitur in 
scriptura contineantur anni lunares et solares et Graecorum et 
Latinorum et hujusmodi, et volumus omnia tempora reducere 
ad annos solares^et ad annos Latinorum,qui sunt anni Christi, 
necesse est nobis in sacra historia scire horum temporum 
diversitatem, et ut sciamus quid est proprium cuilibet et 
quomodo aequantur ad invicem, et quomodo possumus extra- 

^ What follows to the end of the paragraph is omitted in O. 



MATHEMATICAE JN DIVJNIS UTILITAS. 189 

here majus de minori, et contrario, et quodlibet de quoHbet. 
Sed impossibile est hoc fieri, ut exigit scriptura, nisi per 
canones et tabulas et caeteras considerationes astronomiae *. 

Caeterum computantur anni a principio mundi secundum 
Hebraicam veritatem, et computantur secundum LXX inter- 
pretes; sed discordant penitus, et omnes historiae et chronicae 
auctores et sancti hic contradicunt sibi invicem, non solum 
in toto tempore a principio usque ad Christum, sed in aetatibus 
particularibus. Sed diversitas haec non potest certificari, nisi 
per aliquam radicem certam. Nulla vero scientia potest hic 
invenire nec habet unde cogitet de tanta certitudine nisi 
astronomia, cujus est considerare revolutiones certas et ratas 
edipsium et conjunctionum planetarum et caeterarum revolu- 
tionum coelestium, stante ordine naturae. Quapropter oportet 
quod astronomia apponat hic dih'gentiam. Et hoc possumus 
videre per libros astronomorum. Nam Ptolemaeus in Alma- 
gesti certificat nos de tempore a Nabugodonosor usque ad 
Alexandrum, et ab eo usque ad Octavianum Augustum, et ab eo 
usque ad Adrianum principem. Et Ecclesia tenet quod 41"»®* 
anno Augusti fuit Dominus natus. Quapropter per hanc 
viam certificatur multum tempus a Nabugodonosor usque ad 
Christum ^ Et si consideremus sententias Albumazar in libro 
Conjunctionum, videbimus quod ipse ponit principium mundi 
et primum hominem, scilicet Adam, et ab eo numerat annos 
usque ad diluvium, et ponit diem et horam quibus incepit 
diluvium, et per revolutiones planetarum et per eorum con- 
junctiones ieterminat sequentia secula, scilicet quando fuit 
Nabugodonosor, et quando Alexander, ct quando Dominus 
Christus, et quando Mahometus, et sic de multis. Et ideo 
per artem Albumazar et Ptolemaei et caeterorum mathe- 
maticorum oportet resolvere tempora usque ad principium 
mundi, ut^ sciamus quot anni sint a principio usque ad 

^ The whole of Uie foregoing paragraph, except the first two sentences, 
omitted in O. ' Sic in O. J. has xlii. 

' This is g:iven somewhat more fully in Op. Ttrt. ch. 54 (Brewer, p. ao8). 
The time from the creation of Adam to the Deluge is stated to be a,a96 years, 
I month, a3 days, and 4 hours. 

* The following page and half, down to the word dicentes, is omitted in O., 
but is supplied by the two Cottonian MSS. 



creation. 



190 OPERIS MAJORIS PARS QUARTA. 

Christum non solum in summa, sed per singulas aetates ac 
secula. 
Dateof Secundo, possumus persuadere de utilitate astronomiae 

propter temporis principium determinatum, scilicet an a luna- 
tione Octobris seu aequinoctio autumnali, aut ab aequinoctio 
vernali. Nam multi voluerunt secundum sententiam vulgi, 
quod mundus fuerit creatus circiter aequinoctium vernale ; sed 
alii apud aequinoctium autumnale ; quia in veritate secundum 
Hebraicam veritatem, annus, quantum ad seriem temporis 
naturalem, incipit circiter aequinoctium autumnale. Et hoc 
manifeste potest probari per textum Exodi, ubi dicitur, quod 
scenopegia celebretur in exitu anni; id est in mense post 
exitum anni. Nam 23 habetur sic, * SoUemnitatem quoque 
in exitu anni, quando congregaveris omnes fruges de agro.' 
Ergo post principium novi anni tunc incipit. Et 34 de eodem 
dicitur, * Facies sollemnitatem, quando redeunte anni tempore 
cuncta conduntur.' Et in glossa Hieronymi Ezechielis primo 
habetur, quod October est pfimus mensis anni et Januarius 
est quartus. Et Nehemiae primo, * Et factum est in mense 
Casleu, id est Decembri anno vicesimo ' ; et secundo, Factum 
est in * mense Nisan anno vicesimo.' Si enim Nisan, id est 
Aprilis, esset caput anni non diceretur anno vicesimo sed 
anno primo et vicesimo, ut patet. Item, per praecepta de 
seminandis et metendis agris propter quietem septimi anni. 
Nam si Nisan, id est Aprilis, sit caput anni, tunc cum 
seminatur in Septembri vel Octobri sexti anni, non poterit 
meti in septimo anno, quia ferialis est secundum legem, 
et sic peribit seges. Item cum totus annus septimus feri- 
alis est, tunc si incipiatur annus ab Aprili usque ad Sep- 
tembrem non haberent quod comederent, quia fruges sexti 
anni non abundabunt nisi pro septimo anno et pro octavo 
et pro semine octavi, ut dicit Josephus, et non pro nono 
anno. Item per Hieronymum in epistola de solemnitatibus 
illud idem patet. Nam dicit sic, * In fine anni solaris apud 
Hebraeos in septimo mense, quando congregantur fructus 
in horrea sive in cellaria, tunc soUemnia celebrare lege 
praeceptum est, prima die tubarum, decima die expiatio- 
num celebrari debere sabbata. Et a quinto decimo die 



MATHEMATICAE IN DIFINIS UTILITAS, 191 

usquedum finiantur octavae tabemaculorum, feriae esse 
praecipiuntur/ 

Caeterum per Bedam libro temporum, ct praecipue per 
Josephum et omnes Hebraeos a principio usque nunc patet, 
quantum ad initium soUemnitatum, quod Moyses constitutt 
annum ab Aprili propter Pascha, quod est prima soUemnitas, 
et propter mysterium novi temporis, scilicet Christiani, cujus 
anni ab incarnatione computantur, quae fuit circiter aequi- 
noctium, et in quo tempore nunc gloriosum Pascha celebratur. 
Sed in venditione et emptione et caetera gubematione, 
quantum ad anni principium, prioris seculi Moyses decreta 
servavit, ut dicit Josephus primo antiquitatum. Prius autem 
seculum fuit a Moyse redeundo ad principium mundi. Ei^o 
cum principium primi anni mundi et principium mundi fuerunt 
idem, concludunt isti quod mundus incepit circiter aequinoc- 
tium autumnale, ut post spoliationem fructuum veteris anni 
incipiat cultura novi. Haec autem alteratio est gravis valde, 
et ideo recurrunt homines periti ad scientiam cujus est cer- 
tificare tempora, scilicet ad astronomiam. Et illi qui tenent 
primam opinionem volunt se tueri per astronomiam, dicentes 
quod mundus fuit creatus in meliori dispositione propter 
hominis et rerum generationem, et ideo debuerunt planetae 
esse in meliori situ suo respectu gubernationis mundi. Qua- 
propter ponunt quod sol fuit in medio mundi creatus, ut in 
aequinoctiali circulo, ut aequaliter se haberet ad totum mun- 
dum. £t in Ariete eum posuerunt non in Libra, quia dicunt 
astronomi quod sol ibi habeat suam exaltationem, quae est 
major ejus dignitas vel secunda post majorem. Habet enim 
quinque dignitates et fortitudines, scilicet, exaltationem, 
domum, triplicitatem, terminum, et faciem. £t iterum ponunt, 
quod cum oporteat planetas habere eccentricos, necesse fuit 
mundo ut lux solis fuisset in Ariete, quia locus augis est longe 
nobilior quam alia pars eccentrici. Nam quum sol et luna et 
caeteri planetae sunt in augibus suis, tunc sunt fortioris et 
melioris operationis in hoc mundo, sicut determinant astronomi, 
et sicut experientia docet. £t ex his omnibus sequitur 
secundum hos quod mundus incipiebat ab aequinoctio vernali. 
Et quod objicitur eis, quod omnia terrae nascentia fuerunt 



192 OPERIS MAJORIS PARS QUARTA. 

creata in maturitate fructuum, quod non accidit per naturam, 
dicunt quod hoc fuit ex vi creatoris non ex vi naturae, cum 
tamen adjungant quod in multis r^ionibus australibus est 
calor veris magis conveniens pro fructibus maturandis quam 
aestatis. Et non solum in vere, sed iterum in autumno habent 
fructus propter temperamentum aequinoctii utrlusque. Alii 
vero, qui ad plura respiciunt, scilicet ad rationes praedictas de 
principio anni et mundi, efficaces et insolubiles eis qui prae- 
dictam opinionem tenent, istorum sententias nituntur reprobare 
per vias astronomiae. Nam allcgant, quod antiqui astronomi 
ponunt principium anni circiter principium Octobris, sicut 
patet in expositione tabularum, quae Almanac vocantur. Et 
dicunt quod Ptolemaeus invenit certitudinaliter augem solis in 
Geminis tempore suo. Sed si in principio fuisset in Ariete, 
sicut in exaltatione solis, ut in decimo quinto gradu vel decimo 
nono, in quibus ponitur soUs exaltatio, movereturaux secundum 
motum planetarum, scilicet secundum signa contra motum 
primi coeli. Sed hoc non potest esse, quia tunc regiones 
habitabiles super quas est aux fierent inhabitabiles per succes- 
sum temporis, quando scilicet oppositum augis eveniret super 
eas ; et e contrario inhabitabiles fierent habitabiles quod est 
absurdum : propter quod ponunt quod aux moveatur secundum 
motum coeli stellati, non quemcunque imaginatum, sed per 
motum Indorum et Thebit, scilicet per descensum et ascensum 
polorum ejus, vel per motum capitum Arietis et Librae coeli 
stellati in parvo circulo circa capita Arietis et Librae fixa, 
quae sunt in coelo nono. Quo quidem motu capita Cancri et 
Capricorni moventur progrediendo et regrediendo in superficie 
eclipticae zodiaci immobilis nunc ad orientem, nunc ad occi- 
dentem, sicut apparet ex imaginatione Thebit, qui super 
opera Ptolemaei addidit in hac parte juxta sententias Indorum. 
Sic enim assignatur motus octavae sphaerae. Et in hoc 
Arzachel in tabulis et canonibus concordat, et Albumazar in 
libro Conjunctionum, et omnes astronomi sic modo utuntur. 
Sed et sic ponunt augem solis moveri progrediendo et r^e- 
diendo, et ita non recedit a Geminorum signo, propter quod 
non vadit in circuitu terrae, ut oppositum augis aliquando 
contingat terras habitabiles. 



MATHEMATICAE IN .DIVINIS UTILITAS. 193 

Caeterum illi, qui ponunt modo praedicto, scilicet quod sol Position of 
fuit creatus in Ariete, dicunt quod paradisus est sub aequi- *™ *^' 
noctiali propter temperamentum maximum, quia uterque 
locus est nobilior mundi, ut ponunt. Sed si aux fuerit ibi in 
principio mundi, tunc fuit oppositum augis in loco Librae, qua- 
propter in aequinoctio autumnali ejusdem anni fuit sol super 
eadem loca. Quare tunc fuit solutum temperamentum, et 
bonitas complexionis paradisi et regionis totius aequinoctialis 
violata singulis annis, quod est contra proprietatem illorum 
locorum secundum positionem istorum. Nam sic factae sunt 
inhabitabiles cito propter oppositum augis, quia tunc sol est 
prope terram et comburit eam. Sed ipsi volunt quod tem- 
peratior locus mundi sit sub aequinoctiali^ et maxime in 
paradiso, quod stare non potest cum praedictis. Et ideo hi, 
qui sic objiciunt, volunt solem fuisse in Libra, quatenus 
statim peccatum Adae sequeretur poena, ut separatus a para- 
diso non posset pertingere ad ipsum propter combustionem 
regionis ultra aequinoctialem. Et ad hanc combustionem 
faciendam, statim post ejectionem Adae a paradiso usque 
citra aequinoctialem, necesse fuit ut sol foret in Libra, quia 
ibi jam constitutus fuerit versus oppositum augis ultra medie- 
tatem eccentrici, quatenus statim incipiet combustio, quod non 
accidisset in Ariete. Et multae considerationes astronomiae 
sunt hic. Et ideo oportet theologum in hac parte scire bene 
radices astronomiae. 

Et tertio indiget theologus considerationibus astronomiae Longevity 
nunc tactis propter longaevitatem Adae et filiorum ejus^[J^"' 
usque post dies Noae, de quibus loquitur scriptura. Nam 
mirum est quomodo declinavit aetas humana, cum in prin- 
cipio fuit tantae longitudinis et tot tempora transivit. Et 
ideo multi imponunt bonitati constellationis coelestis in 
principio mundi, et circiter hoc. Et investigant illam boni- 
tatem per dignitates planetarum, ponentes, ut dixi, solem esse 
in aequinoctiali et in Ariete et in auge, et planetas alios esse 
in bonis locis et convenientibus aspectibus, ut fortificaretur 
natura humana per bonitatem constellationis a principio, 
quatenus vivere posset ita diu. Sed paulatim deficiente 
bonitate dicta per mutationes situs planetarum et stellarum 

VOL. I. O 



194 OPERIS MAJORIS PARS QUARTA. 

abbreviata est vita hominis ut ad aliquem terminum vcniret 
ultra quem non conting^t transire; quia omnium natura 
constantium est ratio et terminus, ut Aristoteles vult, quem 
terminum ponit scriptura circiter octoginta annos in vigore, 
sed amplius est labor et dolor. Sed jam tactum est, quo- 
modo contra haec objiciunt alii mathematici. Et magna 
disputatio est hic ; et forsan invenietur quod dech'natio aetatis 
non est per recessum a bona mundi dispositione in principio, 
sed ob alias causas determinatas, ut suo loco inferius ex- 
ponetur. 
Datcof Et quarto necesse est principium anni certificari propter 

diluvium. Nam, ut dicit Josephus, diluvium fuit in Novembri. 
Dicit enim haec verba, * Contigit autem haec passio sex- 
centesimo anno nativitatts Noae, mense secundo, qui a Mace- 
donibus Dios nuncupatur, ab Hebraeis autem Maresvan/ 
Sed Dios, ut dicit Beda libro temporum, est November, non 
Maius, ut vulgus aestimat theologorum, et ideo Maresvan 
est November, sicut idem Beda dicit. Et est secundus mensis, 
quia October est primus in naturali ordine temporis, ut prius 
probatum est. Unde Beda dicit, Tisseri enim, qui est October, 
qui Maresvan praecedit, propter collectionem frugum et cele- 
berrimas festivitates, et hunc Tisseri novum annum appellant 
Hebraei. Sic enim Aegypto in annum constituerunt, ut 
Tisseri, id est October, esset principium anni. Et ideo 
magister in historiis * et quidam glossatores non intellexerunt 
Josephum, cum credebant quod Dios et Maresvan essent 
Maius. Et ideo omnes sequentes eos decepti sunt propter 
Graeca et Hebraica vocabula mensium Graecorum et He- 
braeorum, quae non intellexerunt, ut manifestum est inquirenti 
eorum opinionem, qui probant prindpium ahni et mundi fuisse 
circiter aequinoctium anni autumnale. Et ideo hic cadit 
eadem perplexitas, quae prius. Unde necesse est, ut diluvium 
fuerit in Novembri, secundum quod probatum est superius 
tempus naturaliter incipere ab Octobri. Et Josephus hoc 

' This is Peter Comestor (the devourer of books), author of thc Hisioria 
ScholasHcay and commonly called Magister Hisioriarum. Thc Historia SckoiasHca^ 
compiled in the latter half of thc twelfth ccntuiy, bccame the ^4.5^1^111 text-book 
for Biblical stu^ents. 



MATHEMATICAE IN DIVINIS UTILITAS, 195 

evidenter ostendit omni homini, qui scit vocabula Graeca et 
Hebraica de mensibus anni. 

Non solum vero de principio mundi et anni naturaliter 
accidit dubitatio apud theologos; sed de principio diei 
naturalis, an scilicet nox praecesserit diem artificialem vel 
e contrario. Et hoc est quintum hic inducendum circa 
substantiam temporis. Et multi dicunt diem praecessisse 
noctem, et exponunt scripturam ut possunt. Sed secundum 
Hieronymum super Jonam et super Matthaeum, nox praecessit 
diem. Nam, ut ait Alfraganus ^ in astronomia sua, * Omnes 
nationes, quae utuntur mensibus lunaribus, incipiunt diem 
ab occasu solis.' Sed Hebraei et scriptura utuntur mensi- 
bus lunaribus et annis, sicut potest probari modis multis. 
Ergo Hebraei et scriptura utuntur die naturali cujus nox 
praecedit diem. Et ideo tabulae Hebraeorum astronomicae, 
quibus Hebraei usi sunt in certificatione temporum, factae 
sunt ad occasum solis civitatis Jerusalem, sicut tabulae 
astronomorum Latinorum factae sunt ad meridiem civitatis 
Toleti vel alterius. Propter quod in lege determinatur, ut a 
vespera dies incipiat. Nam Levitici xxiii dicitur ' a vespere 
ad vesperum celebrabitis sabbata vestra.' 

Quarta vero radix mathematicae respectu theologiae est (4) Dc- 
penes accidentia et passiones temporum, cujusmodi sunt^*^^^*^^ 
primationes et caeterae aetates lunae et embolismi et hujus- logicai 
modi. Textus enim et expositiones doctorum requirunt ^ 
magnam istorum cognitionem, et maxime secundum Hebrae- 
orum considerationes tam astronomicas quam usuales. DifTert 
autem haec radix a praedicta, quod illa consistit penes sub- 
stantiam temporum, haec vero penes proprietates et accidentia. 
Considerari ergo oportet radicales veritates circa hujusmodi 
passiones, antequam convertatur sermo ad scripturam, quia 
aliter persuasio esset omnino inintelligibilis. Dico ergo 
quod primatio lunae secundum astronomos non dicitur a 
visione novae lunae apud Hebraeos, ut aliqui de theologis 
dixerunt, quoniam hoc tempus non est aequale, sicut ostendit 
Alfraganus. Sed lunatio una aequatur alteri. Aliquando 
enim in mane videtur novacula lunae veteris in suo decremento, 

* See note on Alfraganus in the geographical section 
O % 



196 OPERIS MAJORIS PARS QUARTA. 

et in eodem die in vespere videtur novacula lunae novae. et 
aliquando per spatium trium dierum distant, ut experimentum 
docet et Alfraganus declarat. Et ideo Hebraei antiquitus per 
astronomiam certificaverunt primationem lunae, et cum pon 
fuerat in visione novae lunae, nec potuit per visum cognosd, 
accenderunt faces in Jerusalem in monte alto, ut sciretur quod 
tunc fuit tempus primationis, quatenus homines essent parati 
facere solemnitates et festa quae habebant expedire. Et 
neque consideratur lunatio penes conjunctionem solis et lunae 
veram, quoniam hoc tempus non est aequale, sicut certum est 
astronomis. Sed considerabitur luna penes conjunctionem 
solis et lunae mediam, sicut dicit Alfraganus. Nam hoc tempus 
est aequale semper. Nec tamen dicitur prima luna in con- 
junctione, sed post conjunctionem, quando luna in tantum 
separatur a sole ut sit de se visibih's, h'cet videri non possit. 
Tunc enim est prima accensio lunae, quamvis non videatur 
in illa hora. Et haec diversitas accidit propter latitudinem 
lunae diversam ab orbe signorum, et secundum quod est in 
signis obliqui descensus vel recti, et secundum diversitatem 
regionum septentrionalium et meridionalium, ut docet Alfra- 
ganus in vicesimo quinto capitulo sui libri. Currit autem aetas 
lunae a prima in viginti novem et parum plus. Ex quibus 
aetatibus aggregatur tempus lunationis mediae, seu aequalis, 
quem vocant astronomi Hebraeorum et Arabum mensem 
lunarem, licet aliis multis modis dicatur mensis lunaris. Et 
quamvis peritissimi astronomi in tabulis et canonibus ponant 
tempus aequalis lunationis esse viginti novem dies et triginta et 
unum minuta unius diei, et quinquaginta secunda, ut patet per 
Arzachelem in tabulis Toletanis ; tamen Hebraei astronomi 
consideraverunt subtilius et melius. Tempus enim dictum 
continet viginti novem dies, et duodecim horas, et quadraginta 
quatuor minuta unius horae, sicut opus algoristicum expediet. 
Sed Hebraei dividunt unam horam in mille octoginta partes, 
et quodlibet minutum horae continet octodecim partes horae, 
ut patet cx reductione fractionum unius generis ad fractiones 
alterius. Et ideo tempus lunationis aequalis ^ apud Hebraeos, 

* The mean synodic period of the moon, i. e. the mean period of its rcturn 
to the position in which it b in the same direction with the sun, as determined 



MATHEMATICAE IN DIVINIS UTILITAS. 197 

secundum quod respondet praecise lunationi Arabum, non 
potest esse plus quam viginti novem dies et duodecim horae 
et septingenti nonaginta duae partes unius horae. Sed 
Arabes in tabulis et canonibus computant diminute, et de- 
ficiunt in omni lunatione per tria secunda, et quindecim tertia, 
et quadraginta quatuor quarta, quod patet per examinationem 
legitimam. Et ideo Hebraei astronomi, volentes complere 
lunationem, apposuerunt unam partem, quia minus non 
potuerunt ponere secundum hanc divisionem qua usi sunt. 
Et ideo computant usque nunc in una lunatione viginti novem 
dies et duodecim horas et septingentas nonaginta tres partes 
horae. Et longe certior est eorum consideratio quam astro- 
nomorum utentium tabulis et canonibus apud alias nationes, 
quanquam et plus aliquantulum computant quam praecisc 
exigat lunatio. Nam excedunt in quatuor tertiis et sexdecim 
quartis unius horae. Sed hoc longe minus est quam defectus 
Arabum praedictus. Quapropter satis melius computant 
Hebraei. Nec est curanduni de excessu Hebraeonim prae- 
dicto; quoniam in maximo tempore minimus error contingit, 
et de quo non est curandum. Menses autem Hebraeorum, 
et scripturae usuales diversificantur. Nam unus est triginta 
dierum et alius viginti novem, quia vulgus non potest com- 
putare nisi per integros dies. 

His igitur consideratis propter scripturae et sanctorum Lunar 
intellectum, occurrit consideratio ulterior, ut sciamus quod jj^^ '* 
Hebraei utuntur cyclo lunari, cujus consideratione indiget 
scriptura exponenda. Nam sicut nos utimur cyclo decem- 
novennali, sic ipsi cyclo lunari, cujus primus annus incipit in 
quarto anno nostro. Et ideo falsuni dicunt qui non posuerunt 
Hebraeos uti cyclo ; habent enim embolismos in suo cyclo, 
sicut nos in nostro ; immo nos habuimus ab eis ; et per 
embolismos aequant annos lunares solaribus coUigendo 
undecim dies ter, ut faciant in tertio anno mensem embolis- 
malem, id est superexcrescentem. Et nos hunc modum 
embolismorum traximus ab eis. Et ideo male dicunt famosi 

by calculation from an edipse observed by the Chaldaeans 720 b. c, and from one 
observed in Paris in 1771, is a^, la^, 44'<>, a*-8, a result agreeing almost exactly 
with the value given by the Jewish astronomers. 



198 OPERIS MAJORIS PARS QUARTA. 

viri, qui negant Hebraeos usos fuisse cyclo. Et colligunt 
Hebraei tredecim cyclos lunares et faciunt tabulam et 
canonem ad hoc; qui tredecim cycli continent ducentos 
quadraginta septem annos, quia in tanto tempore redeunt 
omnes observationes festorum legalium ad idem temporis 
principium. Currit igitur observantia l^alis penes hoc 
multipliciter, necnon alia quamplura. Nam neomeniae et 
calendae, in quibus est festum sacrificiorum, et epularum 
solemnium, de quibus dicitur primo Regum xx * Cras calendae 
erunt, et requiretur sessio tua,* exig^unt ut sciamus quod 
mensis lunaris vulgaris incipiat ab occasu soh's. Sed lunatio 
ipsa non habet principium determinatum. Quare si contingat 
luna prima in occasu vel ante in aliqua hora diei naturalis 
praecedentis computabitur in vespera sequente novilunium, et 
neomenia et calendae et novus mensis, quia jam est luna 
prima. Si vero post occasum solis venerit, ut in secunda 
hora diei et ultra, non dicetur illa die naturali novilunium 
nec neomenia nec calendae, quantum ad initium calendae. 
Considerandum tamen quod mensis primus durat ab occasu 
solis primae diei usque ad occasum solis tricesimae diei, et 
tamen lunatio^ non durat nisi a principio noctis usque ad mane 
tricesimae diei quantum ad dies integros, licet aliquae frac- 
tiones sint ultra. Non igitur incipit secundus mensis ante 
occasum solis tricesimae diei, sed lunatio ejus incipit in mane 
tricesimae diei, et ideo duae calendae attribuuntur secundo 
mensi, in quibus fiebant epulae et sacrificia, scilicet in die 
artificiali tricesimae diei mensis primi et in die naturali prima 
et tricesima, quia isti duo dies sunt de lunatione secundi. 
mensis, licet secundus eorum tantum sit pars mensis secundi. 
Propter quod primo Regum xx dicitur, quod sedes David die 
secunda post calendas vacua apparuit. Unde accidit quod 
menses pares habent semper duos dies epularum, sed menses 
impares habent unum tantum. Et ex his patet, quod Ecclesi- 
asticus dicit, *A luna signum diei festi mensis secundum 
nomen ejus est.' Et ex his posset videri an luna fuit prima 
in principio mundi, vel plena, ut multi dixerunt. Nam Judaei 
et scriptura utuntur mensibus lunaribus. Ergo principium 

* luna, J., an erroneous reading. 



MATHEMATICAE IN DIVINIS UTILITAS, 199 

primi mensis et principium mundi fuit idem. Sed mensis 
lunaris a primatione lunae incipit. Quapropter in principio 
mundi luna prima fuit ^. 

Et jam dicta necessaria sunt consideranti egressum Noae de Noah's 
arca, Nam glossae involvunt nos in dubitatione gravi, Jhe a^rk"^ 
propter quod magister in historiis deceptus fuit, cum voluit 
Noae fuisse ^ressum xxviii luna eodem die quantum ad 
calendas quo intravit. Si enim hoc esset verum, tunc non 
tantum per annum, sed per annum et diem ibi fuit, eo quod 
annus solaris constat ex diebus ccclxv, qui complentur a prima 
die Januarii usque ad ultimam diem Decembris, qui est finis 
anni. Et hoc est quod dicit Beda de Temporibus, * Noe cum 
ejus familia decima scptima die secundi mensis arcam 
ingressus et xxvii ejusdem mensis die post diluvium 
egressus asseritur. Claret igitur annum solis integrum, id est 
ccclxv dierum, esse descriptum, quia videlicet luna, quae 
praesentis anni verbi gratia per nonas Maias decima septima 
existit, anno sequentivigesima septima pridie nonas occurret* 
Haec Beda. Quia quota est luna, si undecim addas tota erit 
eadem die, anno revoluto. Ut si hodie est prima, eadem dies 
revoluto anno erit duodecima. Hoc autem verum est, ut in 
pluribus. Tamen aliquando revolutio ejus est tantum 
undecima, aliquando tredecima. De xi, verbi gratia, si hodie 
pridie nonas Aprilis fuerit prima, eadem die revoluto anno 
erit xi. De xiii, verbi gratia, si hodie quinto nonas Maii 
fuerit prima, eadem die revoluto anno erit xiii. Numeret 
quis, et ita per se inveniet. Ista tota intricatio magistri ex 
glossa Strabi exordium sumit. Ut ergo concordemus glossam 
Strabi cum Beda dicimus, quod istud Strabi eadem die debet 
intelligi eadem feria, ut si dominica intravit, dominica exivit. 
Et quod sequitur, si praesenti diei addantur undecim, 
praesenti die computato cum xi, bene dicit, et hoc probatur 
per quod subdit, ideo post annum xi additis, fuit xxvii dies, 
vel xxvii luna. Nam si ipsa dies xxvii excluderetur, non 
xxvii, sicut ipse in glossa ponit, sed xxviii fuisse probare- 
tur. Et hoc sic apparet Nam cum xvii luna secundi mensis 
in arcam ingressus est, patet quod sequenti anno xvi luna 

* CC Op, Tert. ch. 54 (Brcwer, pp. 314-15). 



200 OPERIS MAJORIS PARS QUARTA. 

secundi mensis annus lunaris cccliv dierum expletus est; 
a xvii autem die usque ad xxvii sunt xi dies, qui si praedictis 
cccliv addantur, fiet annus solaris ccclxv dierum, sicut Beda 
superius computavit. Sic ergo egressus est eadem qua in- 
gressus fuerat feria, sed non cadem calenda. Et sic uterquc 
verum dixit. Sed magister tamen dictum Strabi non bene 
glossavit. Quare vero xvii luna intra xi debeat concludi, 
patet per aliam glossam, quae xvii exclusive decem additis 
computat xxvii. Ergo si Strabus computat xi additis tantum 
xxvii et iste, x additis, similiter computat xxvii, patet quod 
ille inclusive, iste exclusive, intellexerit. Cum autem magister 
vult hic excusare se et dare rationem quare dixit egressum 
xxviii, cum Beda dicat xxvii, dicens, *potuit enim esse quod 
vespera xxvii lunae egressus sit, jam imminente xxviii, 
media vero tempora quolibet nomine extremorum saepe 
nominantur'; illud nihil est, quia licet conjunctio solis et 
lunae vera vel media omni hora tam diei quam noctis evenirc 
possit tamen quia Hebraei et Arabes computant secundum 
menses lunares, et luna appropriatur nocti, sicut sol diei, 
ideo dies et menses a vespera incipiunt semper. Et haec 
dicit Beda de temporibus; *Quacunque hora accendatur 
luna, priusquam vespera veniat, non dicetur prima.' Si vero 
post occasum solis accendatur, non prima in praecedenti 
vespera, sed tricesima aestimabitur. 
T>ate of Quod etiam super Exodum de adventu fiHorum Israel in 

Inrsinar^ solitudinc Sinai pro lege Dei recipienda magister dicit, in 
exponendo scripturam xxx dies pro mense ponimus ; hoc est 
falsum. Nam si quilibet numeratur xxx dierum, cum sint 
in anno xii menses, erunt in anno lunari cccix. Sed patet 
quod superflue numerantur vi dies. Constat enim quod in 
anno lunari non sint nisi cccliv, cum annus solaris lunarem xi 
diebus superet, habens ccclxv dies. Ergo in duobus mensi- 
bus non sunt nisi lix dies. Et hoc est quod Beda dicit libro 
de Temporibus, * Nonnullo moveor scrupulo quomodo majores 
nostri diem qua data est lex, quae est iii mensis tertii, quin- 
quagesimam ab agni occisione computent, ponentes primi 
mensis residuos dies numero xvii, quia xiii priores fuerunt 
ante pascha transacti, secundi xxx, tertii iii, qui fiunt simul 



MATHEMATICAE IN DIVINIS UTILITAS. 201 

dies quinquaginta. Et constet duos menses lunares non Ix sed 
lix diebus terminari ; at per hoc in summa temporis memorati 
non plus quam xlix inveniri.' Haec Beda. Igitur secundum 
Bedam prima dies Junii non fuit xlvii, imo xlvi, et sic si lex 
data fuit quinquagesima die a pascha, non fuit data iii die 
mensis Junii, sed iv. Judaei vero dicunt quod die sexta fuit 
lex data, et quarta die adventus eorum in solitudine Sinai. 
Dixit enim Dominus, *Vade ad populum, et sanctifica eos 
hodie et cras, et sint parati in diem tertium.' £t ita iste dies 
tertius fuit sextus eorum adventus ; et secundum hoc quin- 
quagesima die fuit lex data, non incipiendo a pascha, nec 
a prima die azymorum, sed ab altera die azymorum. Et 
hic computus consonat illi de quo habetur Levitici xxiii 
* Numerabitis ab altera die sabbati, id est solemnitatis 
azymorum, in quo obtulistis manipulos primitiarum septem 
hebdomadas plenas usque ad alteram diem expletionis 
hebdomadae septimae, id est, quinquaginta dies.' Hic igitur 
magna involutio invenitur apud lectores propter errorem 
magistri in quantitate mensis et in sua computatione, sicut 
patet consideranti subtilius, et quia nescitur consideratio 
Hebraeorum his temporibus. Et tabula de cyclis lunaribus 
multum rectificat observantias legis. Quoniam secundum 
illam tabulam necesse est, quod licet principium anni sit 
lunatio Octobris secundum veritatem, tamen propter solem- 
nitates legis implendas oportet quod triplicem annum habeant ; 
unum communem, qui est secundum veritatem annus lunaris, 
scilicet habens cccliv dies, et unum diminutum, scilicet qui 
habeat cccliii dies; et unum superfluum, qui habeat ccclv 
dies ; et sic variatur accidentaliter principium anni. Et hoc 
necessarium est,quia in die dominica non potest annus in^ipere. 
Quoniam si in dominica, tunc in xv die mensis septimi esset 
dies dominica, et in vigilia illius festi colliguntur rami de 
arboribus, quod non licet facere in sabbato. Similiter nec in 
die Mercurii nec Veneris potest esse anni principium. Nam si 
in die Mercurii, tunc decima dies mensis esset in die Veneris, 
in quo non licet aliquid facere, quoniam nec cibum parare, cum 
'sit par sabbato. Quapropter tunc oportet eos facere cibaria. 
Majora vero accidunt hic dubitabilia, nisi juvemur magnifice 



202 



OPERIS MAJORIS PARS QUARTA. 



Dates of 
Nativity 
aDd 
Passion. 



per astronomiae potestatem. Nam incidunt quaestiones con- 
tra sententias omnium theologorum Latinorum. Sed propter 
rerum magnitudinem procedam opponendo ad utramque 
partem, et qui potest solvere gaudeat de solutione. Et tamen 
nihil contra opiniones communes Latinorum arguam, nisi quod 
nescio dissolvere. Utinam inveniam qui solvat, si conclusio 
falsa est. Sin autem vera possit ess^ tunc non esset solutio 
necessaria. Sed nullus tantae auctoritatis est in ecclesia praeter 
summum pontificem, qui ausus esset dare sententiam contra 
sententias vulgatas in bac parte quamvis essent falsae. Tenet 
ergo vulgus Latinorum quod Dominus fuit natus secundo anno 
cycli decemnovennalis, et decimo anno cycli solaris, et in his 
non est dubitatio, et quod passus fuit viii calendarum Aprilis, 
et quod luna fuit xv in die passionis, de quibus est quaestio 
magna, atque Latini redai^uunt Graecos, qui posuerunt pas- 
sum Dominum xiv luna. Hoc magistri dicunt omnes, et 
Augustinus, Hieronymus, Beda, dant auctoritates ad hoc. 
Contra hoc potenter arguitur. Nam si viii calendarum 
Aprilis fuit passus et luna fuit xv, non potest hoc esse, ut 
Beda scribit libro temporum, nisi fuisset xiii annus cycli 
decemnovennalis ; et hoc est verum. Quia secundum hoc 
oportuit quod aureus numerus fuerit xiii, ut luna diceretur 
prima in calendario, ubi xiii scribuntur, quatenus ab illo 
loco computetur aetas lunae, ut inveniatur xv in viii calen- 
darum Aprilis; sicut quilibet potest experiri in calendario. 
Sed cum Dominus fuit natus secundo anno cycli, tunc in 
fine illius primi cycli habuit xviii annos secundum cyclum, 
quibus si xiii qui fluxerunt usque ad passionem addamus 
de cyclo secundo, erunt xxxi anni secundum cyclos. Sed 
hi anni secundum cyclum non sunt nisi xxix anni aetatis 
suae, et de xxx quantum est a nativitate usque ad passionem ; 
quoniam prope finem secundi anni ipsius cycH fuit natus, 
scilicet ante principium tertii anni per vii dies tantum, 
quia annus incipit in circumcisione Domini. Quapropter 
in fine primi cycli non habuit Christus annos aetatis suae 
nisi xvii et dies vii, quibus si addantur xiii alterius cydi, 
erunt triginta ; ita quod in xxx fuit passio. Ergo non habuit 
Dominus nisi xxix annos, et tantum de trigesimo quantum 



MATHEMATICAE IN DIVINIS UTILITAS. 203 

est usque ad passionem ; quod est contra evangelium Lucae, 
qui dicit ' Johannem Baptistam baptizasse Jesum incipientem 
quasi xxx annorum.' Et iterum secundum fidem evangeli- 
orum certum est, quod praedicavit pluribus annis. 

Ita Beda nititur probare quod tribus annis et dimidio ultra Theory of 
XXX, ut in xxxiv anno fuerit secundum eum passus, id est, 
xviii anno Tiberii Caesaris. Et alia objectio fortior sequitur ; 
nam si passus fuerit viii calendarum Aprilis et luna fuerit 
XV, tunc, ut prius dictum est, aureus numerus fuit xiii ; 
sed vulgus Latinorum sequitur beatum Dionysium * abbatem 
Romanum, qui primus in chronicis suis instituit annorum 
computationem fieri a Christo, cum prius computabatur a 
tempore Dioclesiani sacrilegi, ut Beda scribit, et certum est ; 
ita, quod transacto dxxxi anno ab incamatione vel nativi- 
tate incipiebat suum cyclum magnum componere, qui tenet 
dxxxii annos, ex multiph'catione cycli decemnovennalis in 
solarem procreatus. Et incipit suum cyclum a dxxxii anno 
post incamationem, et non a dxxxiii, quia Dominus fuit 
natus secundo anno cych', et ideo oportuit novum cyclum 
incipere a dxxxii, scih*cet transacto quingentesimo tricesimo 
primo anno a nativitate. Et quod tantum fuit, Beda docet. 
Nam dicit, * Dionysius paschales scribit circulos, incipiens ab 
anno dominicae incarnationis quingentesimo vicesimo septimo.* 
Si igitur inveniamus literam tabularum, et revolvamus ab ea 
cyclum Dionysii bis et quantum uhra hoc est usque ad annum 
praesentem a nativitate Domini, inveniemus viii calendamm 
in passione esse in dominica, sicut quiUbet potest experiri. 
Sed constat ipsum non fuisse passum die dominica, sed die 

' Dionysius, common]y styled Exiguus, was the first to substitute the era a.d. 
for A. n. c. He placed the date of the Nativity four years later than that accepted 
by previous writers, namely 754 from the foundation of Rome, instead of 750. 
His Paschal Cycle of 533 years, resulted from the multipiication of the lunar 
cycle of nineteen years, and the solar cycle of twenty-eight years. Bede speak- 
ing of the era introduced by him, says (J)€ Umporis roHone^ cap. xlvii), * Primo 
decennovenalis circuli versu temporum ordo praefigitur quem Graeci calculatores 
a Diocletiani principis annis observatore. Sed Dionysius venerabiiis abbas 
Romanae urbis et utriusque linguae, Graecae videlicet et Latinae non ignobili 
praeditus scientia, paschales scribens circulos noluit eis, sicut ipse testatur, 
memoriam impii et persecutoris innectere, sed magis elegit ab Incamatione 
Domini nosiri Jesu Christi annorum tempora praenotare.' 



Marianus. 



204 OPERIS MAJORIS PARS QUARTA. 

Veneris. Quapropter multi diligentes in chronicis, sed prae- 
cipue Beda, et Marianus Scotus, et Gerlandus* famosus apud 
omnes, dubitationem nobis relinquunt maximam penes com- 
putationem secundum cyclos Dionysi. Nam Beda dicit 
computanti^ * Gratias age Deo, si annum passionis Domini sic 
inveneris. Quare si non invenias, incuriae chronographorum 
aut tuae tarditati ascribas.' Et in duobus obviant ei, princi- 
paliter in hoc, quod posuit Dominum esse natum secundo 
anno cycli ; et in hoc, quod posuit praecise dxxxi annum 
transivisse ab incarnatione vel nativitate Domini. 
Theory of Marianus ergo in suis chronicis concedit, quod contingere 
potest, et verum est, quod sit luna xv in viii calendarum 
Aprilis et xiii in annis cycli. Sed tunc vel erit xii annus 
aetatis Christi, vel in cclix ; sed neque fuit passus xii anno 
aetatis suae, neque in cclix. Quapropter non videtur salvari 
posse Dionysius. £t ideo Marianus diligenter attendens 
defectus Dionysii, volens adhuc salvare opinionem Augustini 
et Hieronymi dicit, quia octavo calendarum Aprilis fuerit 
passus, et similiter quod luna fuerit xv, sed non secundo anno 
cycli decemnovennalis, sed xviii, ita quod de illo cyclo sint 
accipiendi duo anni Christi, ut xviii cycli sit primus annus 
Christi, et xix sit secundus, et alter cyclus integer, qui simul 
juncti faciunt xxi annum. Et tunc xiii de tertio cyclo ad- 
dantur et fient xxxiv secundum cyclum. Sed anni aetatis 
Christi sunt pauciores, scilicet xxxii anni et iii menses, et 
bene stant cum hoc numero. Et ideo hic Marianus addidit 
xxii annos ad tempus Dionysii. Et ideo in computatione 

* Bede wrote two works on chronology. Thc first, De temporibus, was com- 
plained of by his disciples as being too short. At their instance, he wrote 
several years afterwards the much more elaborate treatise, De temporum 
ratiotu, 

Marianus Scotus was an Irish monk of the eleventh century who entered an 
Irish monastery at Cologne, and lived subsequently in Fulda and in Maintz. 
He is the author of an universal chronicle beginning with the Christian era, and 
continued to the year of his death in 1082. He considered the Dionysian dalc 
of the Nativity to be twenty-two years too late. Marianus is not to be con- 
founded with the abbot of St. Pcter*s, Ratisbon, a contemporary of the same namc. 

Gerlandus was a student in the Benedictine monastery of Besan^on, of 
which he became prior in 1131. He wrote a Computus (i. e. a work on the 
rectification of the Calendar), and also an arithmetical treatise, mentioned by 
Cantor, voL i. p. 769. 



MATHEMATICAE IN DIVINIS UTILITAS, 205 

nostra a Christo, si volumus sequi Marianum, addemus 
semper xxii annos plures quam computet ecclesia secundum 
Dionysium. Sed secundum Bedam et secundum computa- 
tionem certam annorum imperatorum, manifeste patet Mari- 
anum esse superfluum. Nam secundum eum a nativitate 
Christi usque ad cycluni Dionysii sunt dh'ii; quia ad dxxxi 
jam addit xxii. Sed superius patuit quod ab incarnatione 
Christi usque ad Dionysium non fuerunt tot, sed dxxxi. 
Quantumcunque enim largius computentur anni impera- 
torum, inveniemus quod ipse superfluit in xxii annis, vel 
in xxi, vel ad niinus in xx, et ideo non est imitandus. 
Patet etiam per beatum Augustinum Marianum essc super- 
fluum. Dicit enim Augustinus decimo octavo libro de Civi- 
tate Dei, sic computantur ccclxv anni a passione Christi usque 
in consulatum Honorii et Euticiani. Ergo iste annus, scilicet 
consulatus Honorii et Euticiani, a nativitate est cccxcvii, 
addendo annos a nativitate usque ad passionem, scilicet xxxii 
annos secundum Marianum et iii menses secundum superiorem 
computationem ; sed secundum computationem Mariani, sicut 
ipse in chronicis suis posuit, ccccxix fuit. Constat ergo eum 
esse superfluum xxii annis. Nam si ex ccccxix annis xxii 
dempseris, remanent cccxcvii. 

Gerlandus autem famosus,quem omnes computistae sequun- Theory of 
tur et astronomi in tractando ea quae ad computum pertinent, ^^ "^" 
videns Dionysium non posse salvari nec sequentes ejus, nolens 
etiam Augustino et Hieronymo adhaerere de calenda pas- 
sionis, sed beato Theophilo, qui fuit vicinus apostolis, ponentt 
quod decimo calendarum fuit Dominus passus, dempsit de 
computatione Dionysii vii annos, et posuit Dominum fuisse 
passum nono anno cycli. Nam cum Dionysius posuit Dominum 
natum secundo anno et dempsit unum annum cycli a nativitate 
demit Gerlandus illum i et ii usque ad viii inclusive. Et ideo 
Dominus fuit secundum eum xi annorum, completo illo 
cyclo, quibus si addatur unus cyclus integer et v anni, quia 
V est aureus numerus ut xv luna sit ibi, erunt xxxv anni 
secundum cyclos, et isti bene stant cum annis nativitatis 
Domini. Sed sicut Marianus fuit superfluus, sic Gerlandus 
est diminutus. Nam per computationem superius suppositam 



ao6 OPERIS MAJORIS PARS QUARTA. 

secundum Bedam, et secundum annos imperatorum, a nativitate 
Domini sunt tantum dxxxi vel circiter, ita quod ad minus 
defecit Gerlandus in v annis, quantumcunque largius annos 
imperatorum computemus. 

Magister vero in historiis dubitationibus aliorum apponit 
novum dubitabile. Nam cum dicit in fine capituli de coena 
Domini, * si revolvamus tabulam computi, inveniemus lunam 
xxii in calendis Aprilis et diem Veneris in tempore passionis : 
ergo viii calendas Aprilis fuit xv luna et dies Veneris,' multi- 
pliciter oberrat. Nam si sua sententia esset vera, tunc numerus 
aureus esset xiii, et tunc, sicut prius tactum est, fuisset passus 
ante xxx annos completos, quod est falsum. Item si tabulam 
revolvamus, ut magister dicit, inveniemus G esse literam domi- 
nicalem in tempore passionis, et G esse in viii calendarum. 
Quare fuit passus in dominica, quod est falsum et contra 
evangelium. Sed multi, ut Beda scribit, et maxime Victorius, 
ut patet in epistola sua ad Papam Hilarium de paschali 
observatione, dicunt Christum fuisse passum vii calendarum 
Aprilis et resurrexisse v. Sed tunc, ut Beda dicit, oportet 
quod fuerit annus secundus cycli decemnovennalis, quia binarius 
erit numerus aureus, supponendo quod Dominus fuerit passus 
XV luna, sicut in prioribus semper suppositum est. Sed quia 
XV anno Tiberii posuit Dominum passum, ut ex ejus opus- 
culis patet, ideo merito redarguitur a Beda et aliis. 
The Haec igitur secundum considerationem chronographorum 

wa^oirthe ^^scussa sunt, quae omnia sequuntur ex hoc, quod supponitur 
foorteenth lunam fuisse XV in die passionis. Sed astronomi solliciti in 
moon. ^ h^c parte non possunt invenire xv lunam nec viii calen- 
darum in tempore passionis, nec x nec vii, ita ut ibidem 
inveniatur dies Veneris, quod oportet secundum Evangelia, 
nec etiam a xxx anno Domini usque ad finem vitae suae 
possunt invenire in aliqua calendarum. Quapropter summa 
dubitatio accidit in hac parte. Nam diligenter haec discussi 
tam per me quam secundum consensum peritorum in astro- 
nomia. Sed de xiv luna bene invenitur. Quapropter multa 
secundum scripturam sunt mihi et multis insolubilia in hac 
parte in contrarium, per quae ostenditur quod fuit passus xiv 
luna, sicut Graeci ponunt et Hebraei concordant Nam dicitur 



MATHEMATICAE IN DIVINIS UTIUTAS. 207 

in Matthaeo 'Non in die festo.' Sed dies festus est dies 
azymorum, qui instabat, et dies azymorum est xv. Ergo ante 
fuit occisus. Item Joannes xviii, * Non introierunt in praetorium 
ut non contaminarentur, sed manducarent Pascha.' Ergo in 
vespera proximo ventura manducarunt Pascha ; si igitur 
accipitur ibi Pascha pro agno paschali, in vespera illa in- 
cipiebat xv dies, et fuit luna xv, et tunc computabatur. 
Ergo ante illam vesperam fuit xiv luna. Quare occisus fuit 
Dominus xiv luna, sicut agnus paschalis in lege. Cum 
autem dicitur, quod Pascha ibi non sumitur dicto modo, sed 
aliter, hoc non potest habere auctoritatem ex scriptura, et 
ideo eadem facilitate contemnitur secundum Hieronymum, 
qua probatur. Caeterum cum dicunt Pascha hic accipi pro 
azymis, hoc esse non potest Nam immundi, licet prohi- 
beantur edere Pascha, id est agnum paschalem, non tamen 
prohibebantur edere azyma, si post comestionem agni fierent 
immundi. Immo si aliquis fermentum comederet, dicit lex, 
Exodi xii, quod periret de coetu Israel. Praeterea, nec in- 
veniebatur fermentum in domibus eorum in illis diebus, quare 
tunc non comederent panem per vii dies, quod est omnino 
absurdum. Et ideo non habet haec responsio locum. Item 
Joannes xix, * Erat autem parasceve Paschae.* Ergo eadem 
die ad vesperam paraverunt Pascha. Sed quando paraverunt 
Pascha incipiebat xv luna. Ergo cum fuit passus ante, fuit xiv. 
Item Joannes eodem, * Ibi ergo, propter parasceven Judae- 
orum, quia juxta erat monumentum, posuerunt Jesum.* Ideo 
enim acceleraverunt sepelire, ne in die xv sepelirent, nam in 
die azymorum non sepelissent eum, quia nullum sepeliebant 
in praecipuis festis, sicut sunt Pascha, Pentecoste, Scenopegia, 
et hujusmodi. Item Lucae xxiii, * Et revertentes mulieres,' 
scilicet in die crucifixionis, * paraverunt aromata, et sabbato 
quidem siluerunt secundum mandatum.' Ergo illo die non 
fuit dies azymorum, sed xiv; non enim licuit eis parare 
aromata in die azymorum. Nam Exodi xii de prima et 
ultima die azymorum dicitur, 'Nihil operis facietis in eis 
exceptis his, quae ad vescendum pertinent' Qua ratione 
enim siluissent die sabbato propter mandatum, eadem ratione 
siluissent in die Veneris, si fuisset dies azymorum. Nam 



2o8 OPERIS MAJORIS PARS QUARTA, 

praeceptum cadit super utrumque, licet sabbatum sit sanctius. 
Et Augustinus libro de quaestionibus novi et veteris testa- 
menti dicit, quod fuerit passus xiv luna. Haec autem et 
multa alia hic adduci possunt cum exclusione falsarum respon- 
sionum. 
From this Sed haec nunc sufficiant ut excitemur ad duo, scilicet ut 
astro?'^^^ sciamus quota luna Dominus fuit passus, an xiv vel xv, et 
nomical ^{ una illarum stabiliatur, tunc inveniatur dies passionis per 
shouid be tabulas astronomiae, ut tactum est. Sed haec omnia habent 
the date^* summam difficultatem, magis tamen propter hoc, quod theologi 
ignorant astronomiam et, computum, et hujusmodi, quam 
propter difficultatem rei in se. Si enim essent periti in his, 
pro certo bene invenirent aetatem lunae et diem passionis, et 
mutarent multas sententias quas solemnizant. Nam peri- 
tissimi in istorum consideratione tenent quod Dominus fuit 
passus xiv luna. Et hoc verificato, facile est invenire 
calendas per tabulas speciales ad hoc compositas. Quatenus 
vero excitatio mentis fiat ad hoc, ponam hic unam tabulam, 
in qua secundum tabulas primationum inventa est oppositio 
solis et lunae per omnes annos Domini usque ad xxxviii, ut 
scilicet videatur in quo anno accidit in Martio circiter passio- 
nem Domini, et in quo in Aprili. Non tamen propter certifi- 
cationem hujus rei pono hanc tabulam, sed pro exemplo, ut 
videatur modus persuadendi in hac parte ; nam certificatio est 
valde difficilis propter hoc, quod motus coelorum non sunt 
omnino certificati, nec tabulae qualescunque sufficiunt in hoc 
casu. Multi enim in astronomia periti laboraverunt hic, ut 
has oppositiones solis et lunae invenirent, et non potuerunt 
invenire annum passionis a xxx in xxxv, ubi in Martio 
esset oppositio in die Veneris, nec dies ante oppositionem nec 
proximus post, ita quod cum passione concordaret. Nec ego 
potui invenire adhuc. Ubi tamen poterit oppositio cum die 
Veneris inveniri secundum tabulam praesentem *, patebit per 
ejus expositionem. 

' This is evidently not the table referredto in Optts TerHum, chap. 54 (Brewer, 
p. 215). He says in that passa^e, * [Hebraei] posuenint unam tabulam ex tredecim 
cyclis talibus (i. e. cyclis lunaribus\ qua revoluta complentur omnes, et omnia 
redeunt ad idem temporis principium. £t hic cyclus cum canonibus sub et 
expositionibus est apud eos loci computi et kalendarii apud nos quantum ad 



Principium cycli alia 
via, sc. rationis. 



Principium cycli se- 
cundum computistas. 



Hic. 



Anni Domini. 

Literae sextarum feriarum. 

Dies proximus ante oppositionem. 

Dies oppositionis [et ideo pas- 
sionis signum, et similiter in alia. 
tabula]. 

Dies proximus post oppositionem. 




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16 


28 
29 
30 

31 
32 

33 


d 
a 
d 


e 
b 
e 


- 


32 
41 

50 


36 
24 


e 
c 
b 


a 
c 
g 


b 
d 

a 


c 
c 
b 


14 
23 

32 

57 
5 


56 
44 
32 

4 
52 


34 
35 
.36 


a 

g 
e 


e 
a 

a 
e 


f 
b 
d 


g 
c 
e 


37 
3^ 


■ d 
c 


b 
f 


c 
g 


■ 1 






V T 













April. 
April. 
April. 

April. 
April. 
April. 

April. 



April. 
Mart. 
April. 



April. 
Mart. 

April. 



T^ f^.M A n^ 



MATHEMATICAE IN DIVINIS UTILITAS. 209 



Tabulae explicatio. 

Prima igitur linea in prima tabula inferius occurrens tenet' 
annos Domini usque ad xxxviii ; quia certum est infra hos 
ipsum subiisse passionem. Secunda linea habet omnes h'teras 
feriarum sextarum, quae contigerunt in iUis xxxviii annis. 
Tertia linea tenet dies proximos ante oppositionem solis et 
lunae. Quarta, diem oppositionis. Quinta, diem post op- 
positionem immediate. Sexta, diem sequentem, et sumitur 
hic oppositio solis et lunae media. Septima h'nea cum sibi 
annexis tenet tempus transactum de Martio ante diem pas- 
sionis. Reh'qua vero tabula negotiatur circa Aprilem, ut 
inveniatur oppositio in Aprih circiter diem passionis, excepto 
quod xvii anno et xxxvi accidit in Martio. Sciendum autem 
quod hae tabulae factae sunt ad meridiem civitatis Novariae, 
hcet fuerit facta Parisius ; sed causa fuit, magis enim secreta 
est, et meridies ibi praecedit meridiem Parisius per xxv 
minuta unius horae. Si igitur de tempore habito subtraxe- 
rimus xxv minuta, rehnquetur tempus oppositionis post 
medium diem civitatis Parisius. Secundum ergo hanc tabulam 
passus fuit Dominus iii nonas Aprilis die Veneris in opposi- 
tione solis et lunae mediae xv anno cycH decemnovennalis 
et xiv cycli solaris, anno xxxiii ab incarnatione secundum 
cyclum Dionysii, et hoc est, xxxii secundum veram aetatem 
Domtni. £t istud in tabula secunda accidit super b Hteram 
in directo xxxiii anni post duos dies de Aprili et xvii horas, 
et xvi minuta, et xxxiii secunda, 1 tertia, xxiv quarta, et sic 
sapientissimi in his considerationibus aestimaverunt, qui 

multa. £t hanc tabulam literis Hebraicis misi in Opert Majoti cum ejus expo- 
sitione et canonibus suis, secundum quod pertinet ad computum eorum.* He 
refers to this table again in the following chapter, p. aao. The table given in 
the Opus Majus is the one spoken of in the Opus Tertiumy p. 333. 

What seems probable is that Bacon included with the Opus Majus the 
whole or part of a work written by him in 1263, entitled Computus^ of which 
a good description will be found in Charles's work on Bacon, pp. 336-S. The 
Computus contaius a fuU discussion of the solar and lunar year and month, of the 
lunar cycle of uineteen years and its insufficiency ; and a series of tables com- 
paring the Mahommedan and Christian calendars. 

The table here given contained in the first edition several errors which have 
been corrected by coUation of O. with Tib. 

VOL. I. P 



2IO OPERIS MAJORIS PARS QUARTA, 

multum laboraverunt ad hoc probandum. Unde secundum 
eos, quod viii calendas Aprilis passus fuerit, non est 
opinio ecclesiae certificata, sed vulgata, sicut multa alia 
vulgantur, quae indigent majori certificatione. Si igitur 
oppositio media et xiv luna ab accensione concurrant in 
unum in passione, res manifesta est secundum hanc tabulam 
et secundum aestimationem sapientum. Si vero oppositio 
praecessit in passione xiv lunam per diem integrum, oporteret 
recurrere ad tabulam accensionis novae lunae factam con- 
similiter huic, et tunc magis excluderetur dubitatio. Sed 
hujus rei certificatio, sicut aliorum quae scribo, desiderat 
Ve^trae Celsitudinis assensum, quatenus periti in hujusmodi 
veritatem firmiter stabilirent. Occasionem vero dedi in hoc 
capitulo qualiter ad hujus rei certificationem poterimus 
pervenire, et nego me in praesenti tractatu de tanta diflficultate 
certificasse. 

(5) Gco- Dictum est, quod septem sunt radices mathematicae, quibus 

throws necesse est uti mathematica. Una est de coelestibus. Alia 

light on jg iQ^,jg mundi. Tertia de temporibus quantum ad substan- 

theological tiam. Quarta de passionibus et accidentibus temporum, de 

questions. quijjyg dictuni est. Nunc volo afferre qutntam radicem, et 

est de figurationibus geometricis penes lineas, angulos, et 

figuras tam corporales quam superficiales. Impossibile enim 

est quod sensus spiritualis sciatur, nisi fuerit literalis scitus. 

Sed sensus literalis sciri non potest, nisi homo sciat significata 

terminorum et rerum significatarum proprietates. Nam in 

illis consistit profunditas sensus literalis, et ex eis extrahitUr 

sensuum spiritualium altitudo per convenientes adaptationes 

et similitudines, sicut sancti docent, et patet ex proprietate 

scripturae, et omnes sapientes antiqui sic tractaverunt scrip- 

The Ark. turam. Cum igitur opera artificialia, ut arca Noae, et taber- 

naculum cum vasis suis et omnibus, atque templum Salomonis 

et Ezechielis et Esdrae et hujusmodi alia pene innumerabilia 

ponantur in scriptura, non est possibile ut literalis sensus 

sciatur, nisi homo ad sensum habeat haec opera depicta, sed 

magis figurata corporaliter ; et sic sancti et sapientes antiqui 

usi sunt picturis et figurationibus variis, ut veritas literalis ad 



MATHEMATICAE IN DIVINIS UTILITAS. 211 

oculum pateret, et per consequens spiritualis. Nam in veste 
Aaron, ut dicit scriptura, erat descriptus orbis terrarum et Aaron*s 
parentum magnalia. Et ego vidi Aaron sic figuratum cum ^^^™®™*^- 
veste sua. Sed nuUus posset de hujusmodi corporuro figu- 
ratione cogitare nec ordinare, nisi optime sciret libros Elemen- 
torum Euclidis et Theodosii et Millei^ et aliorum geometrarum. 
Nam propter horum ignorantiam apud theologos non solum 
decipiuntur in maxtmis, sed in minimis. Dicunt enim cum 
magistro in historiis quod sphaerulae candelabri» fuerunt 
corpora circularia, non habentes plenam sphaericitatem. Sed 
non dicuntur sphaerulae diminutive propter hoc, sed quia 
fuerunt parvae sphaerae, habentes tamen completam defini- 
tionem sphaerae Euclidis et Theodosii. Nam Hebraei in 
Gallico suo Hlas sphaerulas vocant pomeas a rotunditate 
pomali et sphaerica, et sic de alifs infinitis. O quam ineffa- 
bilis luceret pulchritudo sapientiae divinae et abundaret 
utilitas infinita, si haec geometricalia, quae continentur in 
scriptura, figurationibus corporalibus ante nostros oculos 
ponerentur. Nam sic mundi malitia diluvio gratiae deleta, 
attoUeremur in sublimi cum Noe et filiis et omnibus ani- 
mantibus suis locis et ordinibus coUocatis. Et cum exercitu 
Domini in deserto excubaremus circa tabernaculum Dei, et 
mensam propositionis, et altare, et sancta sanctorum, ac 
cherubim obumbrantia propitiatorium, et caetera illius antiqui The ubcr- 
populi insignia tanquam praesentia videremus. Deinde temple. 
tabemaculi vacillantis instabtlitate vacuata fixum Domini 
templum Salomonica sapientia fabricatum intraremus. Et 
cum Ezechiele in spiritu exultationis ad sensum intueremur, 
quod ipse tantum spiritualiter intellexit, ut tandem reparata 
nova Jerusalem cum Esdra et Nehemia intraremus majorem 
domum pleniori gloria decorandam. Certe ipsa visio sensi- 
bilis esset pulchra, sed pulchrior quando figuram nostrae 
veritatis videremus praesentialiter, pulcherrima vero quando 

^ Milleius b die Arabic tr&nsformation of MeDcIaus of Alezandria, a mathe- 
matician and astronomer of the first century a. d. Two of his astronomical 
observations, made in the first year of Trajan, are mentioned in the Alntagtsi 
(vii. 3). His work on Spherical Trigonometry (for his discussion of spherical 
triangles may be so called) is not extant in the Greek original, but has been 
preserved in Hebrew aiid Arabic translations. It was edited by Halley in 1758. 

P 3 



212 OPERIS MAJORIS PARS QUARTA. 

scripturae intellectum spiritualem et literalem contemplantes 
gauderemus visibilibus instrumentis excitati, quod scimus 
omnia nunc in ecclesia Dei esse completa, quae ipsa corpora 
sensibilia nostris oculis exhiberent. Et ideo nihil reputo 
dignius studioso in sapientia Dei, quam hujusmodi figurationes 
geometricas ante ejus oculos exhiberi. Utinam jubeat 
dominus quod haec fiant. Et sunt quatuor homines vel tres, 
qui ad haec sufficerent, sed sunt peritissimi Latinorum; et 
merito debent esse periti, quoniam ineffabilis difficultas hic 
latet propter obscuritatem textus sacri, et propter contra- 
rietates sanctorum et diversitates caeterorum expositorum. 
The rain- Scd aliter patet geometrica utilitas respectu sapientiae 
divinae, tam in textu quam in questionibus ; et non solum in 
his, sed in comparationibus pulchris respectu gratiae et gloriae 
et poenae futurae, et cautela vitiorum. De quolibet ponam 
ah*quod exemplum. Et pro omnibus in generali revocemus 
ad memoriam, quod nihil sciri potest de rebus hujus mundi 
sine geometrica potestate, ut prius probatum est. Et rerum 
ccgnitio necessaria est in scriptura propter sensum literalem 
et spiritualem, ut superius expositum est. Nam proculdubio 
tota rerum mundi veritas jacet in sensu literali, ut dictum est, 
et maxime rerum geometricarum, quia nihil est nobis ad 
plenum intelligibile, nisi figuraliter ante oculos nostros dis- 
ponatur ; et ideo in scriptura Dei tota rerum sapientia 
figurationibus geometricis certificanda continetur et longe 
melius quam ipsa philosophia possit exprimere. Nec mirum, 
cum ipse Deus auctor totius sapientiae suam ordinavit scrip- 
turam. Quare pro infinitis exemplis volo unum ad praesens 
afferre. Nam Aristoteles magis omnibus philosophantibus 
nos involvit suis obscuritatibus in tractando de iride, ut nihil 
per eum quod dignum sit inteiligamus, immo multa falsa in 
translatione Latinorum continentur, sicut ex interpretum 
varietate contendimus. Nam quod in codicibus Latinorum 
habetur, quod iris non accidit ad radios lunae nisi in quinqua- 
ginta annis bis, manifeste falsum est, sicut quilibet potest in 
plenilunio quando pluit experiri, dummodo claritas lunae non 
impediatur per nubium densitatem. Et Avicenna dux ac 
princeps philosophiae post Aristotelem, ut clamant omnesi 



MATHEMATICAE IN DIVINIS UTILITAS, 213 

seipsum ignorasse iridis naturam humiliter confessus est. Et 
sic de omnibus philosophis certum est, quod nuUus potuit 
scientiam iridis obtinere. Nec mirum, cum sacram scripturam 
non ita diligenter perscrutati sunt ; sicut fuerat eis necesse. 
Nam omnes philosophi ignoraverunt causam finalem iridis. 
Sed finis iraponit necessitatem eis quae sunt ad finem, ut 
Aristoteles dicit secundo Physicorum, et certum est in omnibus. 
Finem autem, propter quem est iris, solus textus Dei explicat 
evidenter, scilicet, cum dicitur, *Arcum meum ponam in 
nubibus coeli,' &c. Ex quo habetur, quod contra diluvium 
et abundantiam aquarum est arcus Dei ordinatus. Ergo 
oportet, quod quandocunque apparet hic arcus in coelo, sit 
valida consumptio humiditatum aquearum ; et hoc est verum. 
Nam nubes resolvuntur abundanter, et rorationes fiunt in- 
finitae, sicut philosophi dicunt, et nos videmus in magna parte. 
Sed consumptio humiditatis aqueae non est nisi propter 
aliquid quod habeat virtutem consumendi. Nihil autem in 
generatione iridis invenimus nisi radios solis et nubes. 
Nubium congregatio est causa materialis; ergo radiorum 
projectio est causa eflficiens. Sed radii incidentes non possunt 
magnas et mirabiles operationes perficere, quia non concurrunt 
ad invicem ; concursus autem virtutum exigitur ad hoc, quod 
valida operatio educatur. Sed concursus non potest fieri nisi 
per reflexionem et fractionem. Quapropter oportet, quod 
iris generetur per infinitas reflexiones vel fractiones in stilli- 
cidiis infinitis sine intervallo cadentibus, ut sic tam colorum 
quam figurae veritas per hujusmodi multiplicationes penes 
figuras, angulos, ac lineas inveniatur, et non per diversitatem 
matcriae nubis ut in textu Latinorum continetur et omnes 
credunt, sicut certis experimentis explicabo cum de scientiis 
experimentalibus faciam mentionem. Sicut ergo philosophi 
propter ignorantiam scripturae sacrae non potuerunt scire 
veritatem iridis, sic eodem modo impossibile est philosopho 
infiddi attingere ad plenam certitudinem creaturae alicujus 

* Lunar Rainbow. Aristotle's words are {Meteorologkorum^ iii. cap. a) : Ir t$ 

9to9€p iv trvjiv hw\f rii worHiwwra tU kvvr^oi»or pi&rw, Bacon had good cause 
to complain of Aristotelian translation. 



214 OPERIS MAJORIS PARS QUARTA, 

propter scripturae ignorantiam. Nam in veritate quaelibet 

creatura ibi accipitur secundum ultimam sui dignitatem, 

scilicet secundum veram definitionem et descriptionem ejus, 

quia Deus fecit creaturas quas posuit in scriptura, et solus 

ipse scit eas sicut sunt. Cum igitur geometrica potestas 

requiratur ad cognitionem omnis creaturae corporalis, non 

est dubium quin ineiTabili modo valeat sapientiae divinae 

propter rerum cognitionem. 

Expiana- Sed rediens spiritualiter ad propositum pono exemplum de 

Ecci^^^asti- ^C"P^"^^> (\\idiC dicit, *soI tripliciter exurit montes^,' &c. Nam 

cus,cap.43. et incidunt radii infiniti ad omne punctum montis, propter 

^ * ^' quod infiniti exeunt a quolibet puncto solis, et lux est causa 

caloris maxime cum congregatur, ut sensibiliter scimus, et 

infiniti reflectuntura superficie montis, quia a denso fit reflexio, 

et congregantur in omni puncto aeris, et distrahunt omne 

punctum aeris, rarefacientes aerem prope montes, et sic 

secundo calefaciunt montes. £t per medium nubium fran- 

guntur radii duplici fractione, primo in superficie nubium 

versus solem, dein in aere inter nubes et montes. Et per 

hanc duplicem fractionem est necessc omnes radios solis 

venientes ab uno puncto concurrere ad invicem in punctum 

unum in monte vel aere prope montes, praecipue in bene altis 

montibus et Alpibus \ Et sic fiet calor in montibus, licet non 

in altissimis ; quoniam montes qui ascendunt usque ad nubes 

vel prope sicut sunt montes Italiae et Hispaniae, et mons 

Caucasi et Caspiae et alii innumerabiles, habent frigus magnum 

et nives quasi perpetuas ; quia nimis accedunt ad medium 

interstitium aeris, qui est locus frigidissimus in hoc mundo. 

Et sic a singulis punctis solis radii venientes ac dupliciter 

fracti incedunt et augmentant calefactionem montium. Et 

haec omnia patent per figurationes mathematicas, sicut ac- 

cidit de beryllo rotundo vel crystallo, vel urinali, vel quo- 

cunque perspicuo grossiori aere. Quando enim haec corpora 

1 This passage in the Revised Vcrsion is given thus : * A man blowing a 
furnace is in works of heat ; but the sun three times more, burning up the 
mountains :' a rendering which would dispense with Bacon's laborious attempt 
to explain tripliciUr, 

* The iblkming sentence seems to imply that Alps are spoken of in the sense 
usual in Switzerland, of the lower mountain pastures. 



MATHEMATICAE IN DIVINIS UTILITAS. 215 

occumint radiis solaribus, accidit per duplicem fractionem 
quod possit ad oculum et ad tactum eligi punctus aeris post 
hujusmodi corpus, in quo stuppa sicca vel aliquid bene com- 
bustibile accendatur, ut prius habitum est Et haec triplex 
calefactio potest vocari triplex combustio, de qua loquitur 
scriptura ; vel aliter possumus dicere quod facit unam montium 
combustionem de tribus de quibus scriptura intendit, cum 
dicit, 'sol tripliciter exurit montes/ Nam alio modo con- 
sideratur combustio penes varietatem angulorum, quia multi- 
phcatio lucis vel est ad angulos rectos, vel obliquos, vel nuUos. 
Si ad obliquos, est fortis actio ; si ad rectos, fortior est per 
xviii primi Elementorum Euclidis et per alias vias; si ad 
nullos, fortissima propter omnimodam aequalitatem, ut prius 
habitum est Sed ab omni puncto solis ad quodlibet punctum 
montis objecti soli veniunt radii, et infiniti cadunt ad angulos 
rectos, iniiniti ad obliquos, ut manifestum est. Quamvis autem 
superficies montium non est ubique polita et lenis, nec sphaerica, 
tamen in multis partibus ejus est hujusmodi, et infinities per 
portiunculas diversas, et ideo ratione sphaericitatis hujusmodi 
accidit casus ad nullos angulos, et ideo est triplex incidentia. 
Quapropter accidit triplex radiorum casus penes angulum et 
privationem anguli. Et in omnibus modis est calefactio per 
casum lucis et congregationem. Quapropter secundus modus 
combustionis, de quo loquitur scriptura, potest hac via nunc 
dicta assignari. Tertio vero casus lucis variatur penes figuras, 
nam cadit in sphaerica figura et pyramidali cujus conus* est 
in sole et basis in monte, atque in pyramidali cujus conus est 
in puncto montis et basis in sole. Et omnibus his tribus 
modis figuratur multiplicatio luds a sole in monte, ut certum 
est ex supradictis. Sed multiplicatio lucis sphaerica licet 
possit esse fortis, tamen pyramidalis, cujus conus est in sole, 
est fortior ; et pyramidalis, cujus conus est in puncto montis, 
est fortissima, quia, ut dictum est per illam pyramidem a tota 
superficie solis objecta monti venit lux ad quodlibet punctum 
montis, quoniam basis illius pyramidis est superficies solis, et 
infinitae tales pyramides veniunt ab eadem solis superficie, 
sicut manifestum est figuranti. Et natura non requirit plures 
figuras in multiplicatione lucis, nec in alicujus virtutis vel 



2i6 OPERiS MAJORIS PARS QUARTA. 

speciei multiplicatione, ut a quocunque agente fiat spedes mul* 
tiplicanda, ut certum est scienti naturae vias per geometricam 
potestatem. Et per has tres multiplicationes figruratas oritur 
combustio tertia, de qua loquitur scriptura. Sed haec sciri 
non possunt, nisi homo optime sciat potestatem geometricam. 
Propter vero quaestiones pono unum exemplum pro mille, 
ubi geometrica requiritur potestas, licet vulgus non advertat. 
Nam de luce et multiplicatione ejus multa quaerunt theologi, 
scilicet utrum sit substantia vel accidens^ utrum sit corpus in 
medio, utrum subito vel successive feratur in medio et caetera. 
Sed haec nullo modo sciri possunt sine eis quae dicta sunt de 
multiplicatione secundum lineas angulos et figuras. Nam 
multiplicatio lucis est sicut multiplicatio omnis alterius 
speciei cujuscunque agentis. Lux enim in medio est species 
lucis quae est in corpore luminoso. £t ideo regulae, quae 
dictae sunt de speciei multiplicatione sumptae generaliter, 
intelliguntur in luce et in qualibet specie determinata. Cum 
ergo multiplicatio speciei absolute consideratae requirat 
maximam geometriae potestatem, ut prius ostensum est 
abundanter, manifestum est quod ad lucis multiplicationem 
intelligendam eadem geometriae potestas necessaria est, 
quamvis theologi non utantur. 
Symbolic Deinde de spiritualibus rebus exprimendis per res geome- 
din&Srre-^ tricas pono exemplum in gratia et gloria et salvandis ac 
fracted,and damuandis, ut videamus quomodo lineae rectae, fractae, et 
rays. reflexac^ valeant hujusmodi spiritualibus adaptari. Et cum 

gratiae infusio maxime manifestatur per luds multiplicationem, 
expedit per omnem modum ut per multiplicationes lucis cor- 
porales manifestentur nobis proprietates gratiae in bonis, et 
repulsa ejus in malis. Nam in bonis perfectis infusio gratiae 
comparatur luci directe incidenti et perpendiculari, quoniam 
non reflectunt a se gratiam, nec frangunt per declinationem ab 
incessu recto, qui attenditur secundum viam perfectionis vitac. 
Sed infusio gratiae in imperfectos, licet bonos, comparatur 
luci fractae; nam propter imperfectiones eorum non tenet 
gratia in eis incessum omnino rectum. Peccatores autem, qui 
sunt in peccato mortali, reflectunt et repellunt a se gratiam 
Dei, et ideo gratia apud eos comparatur luci repuisae seu 



MATHEMATICAE IN DIVINIS UTILITAS. 217 

reflexae. Sed sicut corporum, a quibus reflectitur lux, quaedam 
sunt aspera, a quibus lux reflexa dissipatur nec apparet; et 
quaedam sunt polita et aequalis superficiei et laevis, a quibus 
fit reflexio sensibilis, ut patet in speculis; sic peccatores 
existentes in mortali peccato sunt dupliciter. Quidam enim 
sunt, qui sic repellunt gratiam, quod nihil boni apparet in eis, 
sed apud se et apud proximos manifestum est quod dissipatur 
totus gratiae efTectus in eis, et isti sunt aperte mali qui peccata 
sua non abscondunt. Alii vero sunt, qui licet boni non sint, 
tamen occultant peccata sua, et apparent boni in conspectu 
hominum, ut hypocritae. Et potest aliter fieri comparatio 
ista. Nam peccatores in hac vita comparantur corporibus 
reflectentibus, ut dictum est, et homines in gratia in hac vita 
comparantur illis quibus est fractio lucis propter imperfectiones 
humanae fragilitatis, quia quantumcunque sit homo perfectus 
in hac vita, tamen habet multas obliquitates, et imperfecta est 
caritas in eo et notitia Dei. Sed existentes in patria com- 
parantur illis rebus quae recipiunt lucem penitus secundum 
rectum incessum omni exclusa dedinatione, quantum possibile 
est creaturae, et quantum exigit ordo divinae justitiae, qui 
reddit unicuique secundum quod meruit. Quoniam vero 
damnati omnino carent gratia et gloria Dei, et glorificati 
ratione imperfectionis meriti in multis atque ex lege creationis 
(cum omnis creatura habeat imperfectionem respectu gloriae 
conditoris) sunt quodammodo imperfecti, potest fieri tertia 
comparatio secundum statum damnatorum et glorificatorum 
et Dei, quatenus apud damnatos teneat omnino comparatio 
lucis reflexae, et apud giorificatos valeat similitudo lucis 
fractae, et divinae gloriae summa rectitudo et perfectio noten- 
tur, quomodo melius probatur trinitas personarum et unitas, 
per incessum lucis directum, secundum quod possumus et 
secundum quod licet nos exemplificare per creaturas ea quae 
sunt apud creatorem. 

Et quod valde notandum est adjungam, scilicet quod im- Geo- 
possibile est beatam trinitatem et cssentiae unitatem aptius symbol of 
a nobis repraesentari in exemplo creaturae sensibilis quam per Trinity. 
res geometricas. Nam in solo triangulo inter omnes res factas 
invenitur unitas essentiae cum distinctione trium occupantium 



2i8 OPERIS MAJORIS PARS QUARTA. 

eandem essentiam. Quoniam idem spatium numero et totum 
capit quilibet de angulis trianguli, ut patet ad sensum, et 
tamen veraciter sunt anguli distincti, quod est mirabile in 
creatura, nec alibi reperitur nisi in summa trinitate. £t cum 
super datam lineam necesse est triangulum aequilaterum col- 
locare, ut prima propositio Euclidis denunciat, quid magis 
proprie potest assumi ut intelligamus quod data persona 
Dei patris necesse est trinitatem personarum aequalium 
exhiberi ? 
Symbolic Haec et hujusmodi multa possunt ex geometricis ad sapien- 
ra^^nal ^^^ salutarem pertrahi, et maxime de decimo libro, ubi 
?nd rationalitas et communicatio quantitatum declaretur. Nam 

nombers. baec et ad divina et ad virtutum iigurationes cum exclusione 
vitiorum utiliter et praeclare possunt adaptari. Nam quic- 
quid de rationabilibus quantitatibus continetur ibi potest 
pulchre et proprie ad vitam rationabilem, quae in virtute 
consistit, facile pertractari. Et quod de irrationabilibus quan- 
titatibus exponitur potest moribus irrationabilibus et bestialibus 
peccatorum conformari. Quicquid etiam de communicatione 
quantitatum dicitur potest convenienter trahi ad actus caritatis. 
Et quod de incommunicatione proponitur, ad odium et 
divisionem animorum noscitur pertinere. Sed longiorem ser- 
And of monem haec requirunt De cautela vero peccatorum magnum 
tio?o^ys. adjutorium est per considerationem hujusmodi geometricarum 
multiplicationum. Nam cum res delectabiles hujus mundi 
sint nobis sicut muscipula, quibus capiamur ad peccatum, ut 
in libro Sapientiae scribitur ; et sicut est in hamo diaboli, qua 
strangulemur, nisi quantum Deus dignatur nos custodire, et 
sensu» nostri super res delectabiles delati nuntiant intellectui 
occasionem peccati ; primum et principale remedium quod in 
homine sit est ut in quinque sensus suos species rerum delec- 
tabilium, ut mulierum, et ciborum, et divitiarum, in quibus 
humana cupiditas aestuat et ambitio superba gloriatur, 
non recipiat secundum multiplicationem principalem ; nam 
accidentalis sufficit homini ad damnationem, quando recipitur 
avide et abundanter. Sed magis adhuc cavenda est multipli- 
catio recta sensibilis quam fracta vel reflexa, propter fortiorem 
actionem prius expositam. Maxime vero, ne species delecta- 



MATHEMATICAE IN DIVINIS UTILITAS. 219 

bilis recta cadat ad angulos aequales in sensum, quia tunc 
fortissima est, praecipue si conus pyramidis brevis occurrat. 
Sic Eva recepit speciem soni serpentis et pomi visibilis et 
suavis odoris. Et Adam allectus est ut se et totum genus 
humanum specierum sensibilium multiplicatione damnaret. 
Sic David sanctus propheta per speciem Betsabeae deceptus 
de adulterio cecidit in homicidium. Sic senes presbyteri 
quos judicavit Daniel specie mulieris decepti sunt Et certum 
est omnem hominem decipi speciebus rerum hujus mundi ; 
quia secundum Johannem, * omne quod est in mundo, vel est 
concupiscentia camis, vel concupiscentia oculorum, vel superbia 
vitae,' a quorum amore nullus se potest abstinere, qui gaudet 
in sensu specierum quae veniunt a rebus. Nam capitur sicut 
bestia. Et ideo homines sanctitati vacantes avertunt sensus 
ab omnibus rerum delectabilium speciebus quantum possunt, 
et maxime de illis quae pertinent ad sensum tactus et gustus, 
quae sunt gulae et luxuriae, ut non solum non tangant, sed 
nec videant nec audiant de his iieri mentionem, ne species 
multiplicata in sensus spiritum cogat servire carnis illecebris ; 
et praecipue cavent ne prope sint, ut vitent pyramides breviores, 
atque multiplicationes principales et rectas et ad angulos 
aequales, ut praedixi. Et haec maxime cavenda sunt quando 
oportet vel in confessione vel ob aliam aliquam causam loqui 
cum mulieribus. Nam omnes homines quantumcunque sanctos 
species fortes in hac parte turbarent, etsi non vincerent quos 
Deus custodire dignatur. 

Jamdictum estdequinque radicibus mathematicae respectu (6) Sixfold 
scripturae ; nunc remanent nobis duae aliae, scilicet numeri et of Mkh- 
musicalia. Quoniam vero sancti abundanter ostendunt utili- ^^^^ ^ 
tatem istorum respectu theologiae, et magis exprimunt horum ^' 
comparationes et laudes respectu divinorum quam de prioribus, 
ideo plura de aliis tetigi, et de his solum innuam quasdam 
vias, quarum explicatio in libris sanctorum copiose invenitur. 
Numeri vero ad sensum scripturae valent quatuor modis. Nam 
non est numerus in scriptura positus, quin accipiatur in sensu 
literali secundum omnes ejus proprietates arithmeticas, qua- 
tenus per congruas similitudines eliciantur sensus spirituales, 
sicut sancti infinitis quasi modis manifestant. Secundo, propter 



220 OPERIS MAJORIS PARS QUARTA. 

historias sciendas et certificandas necesse est theologum 
abundare in potestate numerandi, ut sciat omnes modos 
algoristicos, non solum in integris sed in fractionibus> quatenus 
sciat numerare, addere, minuere, mediare, multipHcare, dividere, 
et radices extrahere, tam fractiones quam integra ; et iterum 
quod non solum sciat vulgares fractiones penes medietates, 
tertias, quartas, quintas, et sic in infinitum ; sed quod sciat 
astronomicas fractiones per minuta, secunda, tertia, quarta, 
quinta, et sic in iniinitum; quia in his historialibus oportet 
recurrere ad motum solis et lunae, in quibus tales fractiones 
considerantur principaliter, de quibus satis exemplificatum est 
superius. Et non solum oportet fractiones Latinorum scire 
et Arabum, sed Hebraeorum, qui frang^nt unam horam in 
mlxxx partes de quibus tactum est prius. Caeterum illum, 
qui uti debet his, scire necesse est reducere diversa genera 
fractionum ad invicem ; quia si inter integra accidant septem 
quintae, et decem septimae, et viginti octavae, et hujusmodi 
infinitis modis, non potest homo se expedire, ni istas diver- 
sitates fractionum reducat ad unum genus fractionis, ut sic 
reducantur ad integra. Sed in his fractionibus et integris 
utendis magna est subtilitas, et pulchra sapientiae lumina 
relucescunt, praecipue cum per haec tota sapientia divina et 
humana dirigitur et rectificatur, secundum quod auctoritates 
Cassiodori et Isidori prius manifeste expresserunt, qui crude- 
liter nos redarguunt ex eo, quod omnes ignorantes numerorum 
potestatem asserunt non differre a brutis animalibus, quae nec 
divina nec humana cognoscunt. Tertio, valet consideratio 
numerorum in scriptura, scilicet in divisione et distributione 
sortium praedarum et portionum facienda sacerdotibus, Levitis, 
principibus, et singulis, secundum quod Moyses peritissimus 
in numerationibus algoristicis distribuit unicuique quod suum 
est, infinitam quasi multipiicationem rerum distribuens in 
partes certissimas operibus algoristicis propriissimis tam in 
fractionibus quam in integris. Et nullus literalem sensum, 
nec per consequens spiritualem potest elicere, ut exigit dig- 
nitas scripturae, nisi operum horum sciat rationem et noscat 
operationes numerandi per quas Moyses et alii in scriptura 
procedunt. 



MATHEMATICAE IN DIVINIS UTILITAS. 221 

Quarto^, necesse est optime scire rationes numerandi propter Arith- 
corruptionem numerorum in scriptura, quia quasi infinitis ^^j*^\, 
modis corrumpuntur ; fere enim omnes numeri sunt comipti. received 

r^ ... - . . . vcrsion of 

Quae comiptio ad ventatem reduci non potest, nisi per Bibie. 
omnimodam numerandi potestatem tam in fractionibus quam 
in integris. Fere enim aut pro majori parte omnes numeri in 
sacro textu et in Hbris sanctorum sunt scriptorum et cor- 
rectorum vitio depravati, de quibus pauca exempla subjungam 
pro infinitis. Nam undecimo capitulo Genesis habetur, 
* Vixit Arphaxat, postquam genuit Sale, ccciii annis.' Sed 
in Hebraeo habentur cccciii anni. De Graeco vero non 
potest haberi veritas, quia inter Arphaxat et Sale interponit 
Cainan, quem nos non habemus, sicut nec Hebraeus. Et 
in eodem capitulo, *Vixit Reu xxxii annos' secundum 
Hebraeum et antiquos codices Latinorum. Sed in exemplari 
vulgato habentur xxxv, ut historiae veritas continuari non 
possit. Et xviii capitulo in penultima parte ejus, ^Quid si 
minus quinquaginta justis quinque fuerint, delebis propter 
quinque.' Sic Hebraeus, sic antiqui Ubri habent. Modemi 
autem posuerunt xlv propter sensum planiorem. Sed non 
licet sine sede apostolica mutare textum quem recepit et jussit 
per omnes ecclesias derivari. Et xxxvii capitulo, *Joseph 
cum esset xvii annorum ' secundum Hebraeum et Graecum. 
Sed moderni habent xvi, et quod in eodem capitulo non 
sit venditus xxx argenteis, sed xx, probatum est superius 
multiplici testimonio. Et in Exodi xiv capitulo, *tulitque 
sexcentos curru«,' secundum Hebraeum et Graecum et 
Josephum et antiquos codices. Sed pars glossae truncata fere 
in omnibus h'bris facit quod exemplar vulgatum habet ccc 
currus. Nam communiter habetur hoc tantum in glossa 
*contra fidem trinitatis pugnatunis.' Unde propter nomen 
trinitatis abraserunt sexcentos et posuerunt ccc. Sed in 
pluribus antiquis glossatis invenitur sic, ' contra fidem trinitatis 
numero senario se armavit pugnaturus.' Et ideo secundum 

' This paragraph supplies further illustralioiis of the corruption of the Paris 
text of the Bible, spoken of on p. 77, and also in the Opus Minus (Brewer, 
pp. 330-349). It is also one of many proofe of the care with which Bacon had 
collated the Septuagint and the Hebrew text 



222 OPERIS MAJORIS PARS QUARTA. 

glossam possunt ibi esse sexcenti. Et Exodi xxxii habetur 
in Hebraeo et Graeco 'quasi tria millia.' Sed exemplar vul- 
gatum habet viginti tria millia. Et dicit magister in historiis 
quod hoc est de antiqua translatione. Sed antiqua translatio 
est LXX interpretum, et est de Graeco, Graecus autem non 
habet hoc, sed sicut Hebraeus. Et hic error habet apparen- 
tiam ex prima ad Cor. x. Sed non est intelligendum pro 
hoc loco, ut patet in textu et in glossa. Quoniam cum dicit, 
* Neque idololatrae efficiamini,' &c. quod ad hunc locum per- 
tinent, non ponit numerum interfectorum. Sed statim cum 
dicit, * Neque fornicemur ' &c. sequitur, * et ceciderunt viginti 
tria millia,' quod intelligitur secundum glossam de his, qui for- 
nicati sunt cum Madianitis, ut I^itur xxv Numerorum. 
Nolo plura exempla aggregare ad praesens, cum non sit ex 
principali intentione corruptionem textus probare. Sed haec 
ideo intuli, ut videatur necessitas computandi in scriptura, 
quatenus sciamus verificare corruptiones numerorum. 
Propcrtics Et adhuc potest quinta ratio de numerorum utilitate signari. 

of number _- . . , , . . • i 

three. Nam unitas in se ducta cubice, id est, ter, ut semel unum 
semel non multiplicat essentiam, sed eadem manet licet aequa- 
litate trium laterum deducatur. Et sic familiari exemplo 
theologi notant beatam Trinitatem. Quamvis autem multiplex 
numeri perfectio inveniatur secundum quod denarius dicitur 
esse perfectus, et septenarius, et senarius, tamen maxime 
temarius sibi vindicat perfectionem ; quoniam perfectio 
praecipua quae numeris aliis attribuitur est quod omnes partes 
aliquotae simul sumptae reddant suum totum, ut patet in 
senario. Sed in temario solo accidit, quod pars aliquota et 
non aliquota simul sumptae reddunt ipsum, scilicet unitas et 
binarius, quod non potest in alio inveniri. Atque cum in 
omni numero sint duo, scilicet discretio partium et unitas 
congregationis eamm^ qua numerus dicitur esse unus; nec 
aliquid aliud facit numerum nisi haec duo ; ista praecise re- 
periuntur in temario. Per binarium enim est discretio, et per 
unitatem ipsa unitas habetur. Et ideo tota perfectio numeri 
in temario et non in alio reperitur. Et propter hoc hic 
numerus convenit creatori magis quam alius. Et sicut ab 
unitate omnis multitudo procedit, sic ab ipso Deo. Et arith- 



MATHEMATICAE IN DlVlNlS UTILITAS. 223 

metica docet in fine suo omnes medietates investigari in Three 
proportionibus numerorum. Nam nec geometra nec musicus ^^^1011. 
nec astrologus de his tractat, sed supponit quod arithmetica, 
quae est scientia numerorum, edocet. Theologi autem 
nituntur has medietates ad proprietates divinarum persona- 
rum exaltare, et praecipue Ricardus de Sancto Victore in 
libro de trinitate^ qui liber magnam habet difficultatem ob 
istarum medietatum ignorantiam apud vulgus. Et multi 
propter eandem abutuntur comparationibus istarum medie- 
tatum ad divina. Triplex vero est medietas, scilicet arith- 
metica, geometrica, musica. Arithmetica vero consistit in 
identitate diflerentiarum primi ad secundum, et secundi ad 
tertium, ut quatuor, tria, duo. Nam unitas sola est differentia 
hinc inde, et huic simile reperitur in divinis personis. Nam 
differentia Patris ad Filium est quod Pater dat Filio et non 
accipit ab eo ; Filius autem e converso. Similiter inter Filium 
et Spiritum Sanctum est consimilis differentia. Nam Filius 
dat Spiritui Sancto et non accipit ab eo ; Spiritus autem 
Sanctus e converso accipit ab eo et non dat ei. Et cum geo- 
metrica medietas sit, quando est eadem proportio primi ad 
secundum, et secundi ad tertium, ut inter viii, iv, ii, ratio 
hujus medietatis per omnimodam aequalitatem et unitatem 
essentiae in tribus personis reperitur, et in omnibus essentia- 
libus, quae sunt potentia, sapientia, bonitas. Nam credimus 
et firmiter tenemus quod qualis est Pater talis est Fih'us, et 
tah's Spiritus Sanctus. Harmonica seu musica medietas con- 
sistit in identitate proportionis primi ad tertium, et diflferentiae 
primi et secundi ad differentiam secundi et tertii, ut vi, iv, 
iii. Nam dupla proportio est inter primum et ultimum ; 
similiter inter binarium, qui est differentia primi et secundi, 
et unitatem, quae est difTerentia secundi et tertii. Et 
sic per similitudinem in personis divinis reperitur. Nam 
quae est proportio Patris ad Spiritum Sanctum quantum 
aequalitas ; sic est inter difTerentiam Patris et Filii, et inter 
difTerentiam Filii et Spiritus Sancti. Nam inter Patrem et 
Fihum est diflferentia, quod Pater dat et non accipit, Filius 
accipit et non dat ; et haec eadem est inter Filium et Spiritum 
Sanctum, ut patet Sic igitur breviter assignantur hae 



224 OPERIS MAJORIS PARS QUARTA. 

medietates, quamquam et aliter a multis assignentur, quos 

non possum intelligere ; quia videtur mihi quod non possunt 

secundum arithmeticae judicium salvari. Sed non est tem- 

poris praesentis opiniones singulorum explicare. 

Dimen- Et sexta ratio de utilitate arithmeticae potest sumi in 

h(»4nly scriptura penes res hujus mundi, quibus ipsa utitur. Nam 

bodies. altitudinem et magnitudinem et spissitudinem et numerum 

coelorum et stellarum tangit et requirit certificationem 

istorum Et sancti in expositionibus suis multa loquuntur. 

Nam Hieronymus dicit super Isaiam, quod Orion habet xxii 

, stellas, quarum ix primae sunt in tertia magnitudine, et ix 

residuae in quarta, et iv ultimae in quinta mag^itudine^ et 

non exponit se. Oportet ergo theologum haec non ignorare. 

Sed specialiter arithmetica rectificat in his, et ideo volo hic 

has veritates magnificas aperire per numeros, quatenus 

pulchre et utiliter apparet comparatio numerorum. Ad hoc 

autem considerandum necesse est ponere aliquam radicem 

Teirestrial ^otam. Haec autem est quantitas arcus terrae, quae re- 

arc wrre- spondet uni gradui in coelo, secundum quod docet Alfraganus 

to a capitulo viii. 

degree. g^ Averroes consentit in fine secundi Cocli et Mundi. Isti 

vero dant modum certificandi hoc in numero milliariorum et 
partium ejus. Ptolemaeus autem quinta Almagesti dictione 
procedit per viam demonstrationis diffuse in quantitate alti- 
tudinum solis et lunae et in eorum magnitudine. Sed non 
dat quantitatem certam per numerum milliariorum ; nec de 
aliis corporibus coelestibus determinat quantitatem. Oportet 
igitur supponere, quod cubitus aequalis et geometricus con- 
tineat pedem et dimidium, et milliare continet 4,000 cubi- 
torum, et sic accipit Alfraganus in sua consideratione. Omnis 
autem circulus sphaerae potest dividi in 360 partes, quae 
gradus vocantur. Intelligamus igitur maximum circulum in 
sphaera coelesti, qui transeat per centrum et dividat sphaeram 
in duas partes aequales. Dico ergo quod uni gradui^ istius 

^ The first attempt to compare angular astronomical magnitudes with terrestrial 
distances was that of Eratosthenes (b. c. 276-196), who found that when the 
sun was vertical at Syene, it was one-fiftieth part of a great circle (i. e. 7° loT) 
from the zenith at Alexandria. The distance between the two places was 



MATHEMATICAE IN DIVINIS UTILITAS, 225 

circuli in coelo respondebunt multa milliaria in terra, cujus 
experientiam innuit Alfraganus in hoc, quod accepta in aliquo 
loco elevatione poli super horizonta, si perambuletur ad 
septentrionem vel meridiem, usquequo elevatior polus appareat 
vel depressior per gradum unum, invenitur quantitas milliari- 
orum terrae, quae respondeat uni gradui in coelo. Nam si in 
nocte clara stellata quis per foramina quadrantis vel astrolabii 
vel alterius instrumenti perspexerit stellam nauticam et ipsum 
polum, et notaverit gradus quos attingit extremitas virgae in 
dorso astrolabii vel filum in quadrante, processeritque in terra 
ad septentrionem donec in altera nocte stellata viderit eundem 
polum elevari plus super horizonta per unum gradum, ille 
arcus terrae, quem perambulaverit, respondebit uni gradui, et 
erit ei similis, ut sumuntur arcus similes in sphaeris diversis 
secundum Theodosium, sed non erunt propter hoc aequales. 

Cum autem per semidiametrum terrae, quae continet 3,250 Dimen- 
milliaria, doceat ai® capitulo mensurari diametros orbium ^°Earth. 
coelestium et distantias augium et oppositorum earum, oportet 
quod veram quantitatem semidiametri accipiat. Nam aliter 
magnus accideret error in distantiis augium, eo quod quantitas 
semidiametri terrae multotiens replicata faceret magnum 
errorem in illis distantiis, nisi praecise sumeretur. Cum 
igitur fatendum est Alfraganum percepisse hunc errorem, 
manifestum est quod ipse accipit veram semidiametri quanti- 
tatem, scilicet 3,250, et veram diametrum, scilicet 6,500. Ergo 
oportet quod supponat radicem veram et completam, quae 
est in quantitate arcus terrae respectu gradus coeli^ licet non 
exprimat eam perfecte. Quapropter ipse supponit quod sit 
56 milliaria, et duo tertiae milliarii, et 27 nonagesimae, et una 
sexcentesima tricesima, vel 56 milliaria et 2,984 cubiti et 

regarded as 5,000 stadia. But the uncertainty as to the Greek measures of 
length, and the coarseness of their astronomical instniments ;indcpendent]y 
of the fact that Alexandria and Syene are not on tbe same meridian), make it 
imposslble to deduce any precise result from this obscrvation. The Arabian 
instruments were better, but were obviously insufficient as a basis for solving 
the problem here discussed by Bacon, of the £arth*s magnitude. 

It may be noted here that in the oldest MSS. of the Opus MaJHs^ as well as in 
those of a later date, Arabic numeials are very commonly employed in dealing 
with large numbers. 

VOL. I. Q 



226 OPERIS MAJORIS PARS QUARTA. 

quinque septimae unius cubiti. Et ideo, si quis bene con- 
sideret, ipse rcspectu diametri et semidiametri, quibus utitur, 
omittit octavo capitulo in hac radice, quae est quantitas arcus 
terrae respectu gradus in coelo, 50 * sexcentesimas tricesimas 
unius milliarii, sive quod idem est, 317 cubitos, et tertiam 
cubiti, ^8 sexagesimas tertias unius cubiti, quoniam non 
exprimit ibi nisi quod arcus iste terrae est 56 milliaria et 
duae tertiae unius milliaris. Sed licet radicem plenam sup- 
ponat, tamen fractiones aliquas omittit propter taediuni 
numerorum. Mos enim ejus est in libris suis multotiens 
omittere fractiones et similiter faciunt alit autores. Si igitur 
volumus huic quantitati diametri, scilicet 6,500 qua utitur, 
adaptare radicem, dicemus quod arcus terrae respondens uni 
gradui in coelo continet 56 milliaria, et duas tertias unius 
milliaris, 27 nonagesimas milliarii, et unam sexcentesimam 
tricesimam. Et si volumus computare per cubitos, erit arcus 
terrae respondens uni gradui in coelo 56 milliaria, et duo 
millia cubitorum, nongenti octoginta quatuor cubiti, et 8 
sexagesimae tertiae unius cubiti, quae 8 sexagesimac tertiae 
sunt plus quam una octava cubiti pcr unam quingentesimam 
quartam unius cubiti, quod de facili patet. Nam octo sexa- 
gesimae tertiae valent 64 quingentesimas quartas, et 63 
quingentesimae quartae sunt octava totius; ei^o 64 quin- 
gentesimae quartae excedunt octavam in una quingentesima 
quarta ; et ita octo sexagesimae tertiae unius cubiti ex- 
cedunt octavam ejus in una quingentesima quarta. Et si 
triplicaverimus diametrum hanc 6,500 et ejus septimam 
addiderimus, habebitur circumferentia totius terrae, et erit 
praecise viginti millia milliariorum quadringenti et viginti octo 
milliaria, et duo millia ducenti octoginta quinque cubiti, et 
quinque septimae unius cubiti ; vel penes alias fractiones, 
crit numerus hic vigesies mille quadringenti viginti octo 
milliaria, et quatuor septimae unius milliarii. Et secundum 
hoc tota terrae superficies erit centies trigesies bis mille 
millia milliaria sexcenties mille milliaria. Et secundum hanc 
radicem perfecte computatam erit quarta terrae habens 
33» 150,000 milliaria in sua superficie. Et octava terrae 

^ The omission is greater than Bacon states ; i. e. it is Ht of a mile. 



MATHEMATICAE IN DIVINIS UTILITAS. 227 

habebit 4,143,750 milliaria. His enim duabus quantitatibus 
indigemus, sicut et caeteris praedictis. 

His visis, consideranda est altitudo coelestium, et similiter Dimeii- 
magnitudo et spissitudo. Nam Alfraganus dicit xxi capi- ^^tial*^^ 
tulo, quod Ptolemaeus et alii sapientes posuerunt medie- spberes. 
tatem semidiametri terrae esse quantitatem qua metiti sunt 
longitudines a centro terrae, et posuerunt corpus terrae 
quantitatem qua mensuraverunt corpora stellarum. Et hoc 
satis patet ex demonstrationtbus Ptolemaei quinta dictione 
Almagesti. Sententiat ergo Aifraganus cx comparatione 
semidiametri terrae ad semidiametrum orbis stellati, quod 
distantia ortns stellati a centro terrae est vigesies millies 
centies decies aequalis medietati diametri terrae, quod est 
sexaginta quinque mille millia trecenta quinquaginta septem 
millia quingenta milliaria, quod si duplicetur, erit diameter 
totius orbis stellati scilicet 130,715,000 milliaria. £t cum 
multiplicatur hoc in tria et septimam diametri erit rotunditas 
maximi circuli in coelo stellato, scilicet 410,818,571 milliaria, 
et tres septimae milliarii, hoc est, 1,714 cubitr, et 2 septimae 
cubiti. £t si hunc numerum diviserimus in 360 partes, una 
pars, scilicet quae erit quantitatis unius gradus coeli stellati, 
habebit milliarta 1,141,162 et 251 trecentesimas sexagesimas 
milliarii, hoc est 2,788 cubiti, et octo nonae unius cubiti. £t 
si duxerimus diametrum in rotunditatem, erit superficies totius 
coeli stellati, 53,7^x5,149,508,265,000, videlicet^ quinquagesiea 
ter millesies millesies millesies millesies mille millaria, septin- 
gentesies millesies millesies millesies mille milliaria, centies 
quadragesies novies millesies millesies mille milliaria, quin- 
gentesies octies millesies mille milliaria, ducenties sexagesies 
quinque millia milliaria^. Semidiameter autem coeli stellati 
est longitudo longior orbis Satumi, quia junguntur sine 
medio. Sed ejus long^tudo propinquior terrae est 46,816,250 
milliaria, quod est longitudo longior orbis Jovis, cujus longi- 

' The manipulation of these lai^ge numbers is interesting; and they may, 
perhaps, to some extent account for the contentment of the ancient and medi- 
aeval mind with a limited universe. Archimedes, in his PsammUes, had assigned 
a wider limit for the diameter of the universe ; viz. ten thousand million stadia, 
or one thousand million miles, as against one hundred and thirty million in the 
computation of Alfinganus and Bacon. 



228 OPERIS MAJORIS PARS QUARTA. 

tudo propinquior est 28,847,000 milliaria, quod cst longitudo 
longior orbis Martis, cujus longitudo propinquior est 3,965,000 
milliaria, quod est longitudo longior orbis solis, cujus longitudo 
propinquior est 3,640,000, quod est longitudo longior Veneris, 
cujus longitudo propinquior est 542,570, quod est longitudo 
longior Mercurii, cujus longritudo propinquior est 208,541 et 
duae tertiae milliarii, et hoc est 2,666 cubiti et duae tertiae 
cubiti, et haec est longitudo longior Lunae, et haec, ut dicit 
Alfraganus, est 64 vicibus et sexta vicis unius aequalis medie- 
tati diametri terrae, et longitudo propinquior Lunae est 109,037 
et medietas milliarii, hoc est, 2,000 cubiti, et haec est 33 vicibus 
et semis et medietate decimae, id est, una vicesima unius vicis 
aequalis medietati diametri terrae. Diametri quidem singu- 
lorum orbium habentur per duplum semidiametri ; rotunditas 
cujuslibet habetur per triplicationem diametri cum additione 
septimae partis, et tota superficies cujuslibet orbis habetur per 
ductum diametri suae in rotunditatem suam, ut exemplificatum 
est in terra et in orbe stellato. Et quilibet potest haec experiri 
per computationem, et ideo omitto haec propter prolixitatem. 
Quoniam vero subtracta longitudine propiore a longiore 
remanet spissitudo orbis, ideo patet, quod spissitudo orbis 
Lunae est 99,504 milliaria, et spissitudo Mercurii 334,209, et 
Veneris 3,097,250, et Solis 325,000, et Martis 24,882,000, et 
Jovis 17,969,250, et Saturni 18,541,250. Haec ex radicibus 
Alfragani et Ptolemaei in Almagesti sumuntur. 

Sciendum vero quod in omnibus istis altitudinibus sumitur 
distantia a centro terrae. Unde licet sapientes aliquando 
dicant long^itudines has fieri a terra, intelligunt tamen quod 
a centro terrae, quia medietas terrae nihil facit sensibile. 
Cum ergo longitudo propinquior orbis Lunae sit 109,037 mil- 
liaria et medietas milliaris, subtracta medietate diametri terrae, 
quod est 3,250, a numero praedicto integrorum milliariorum, 
scilicet 109,037, relicta medietate, residuum distantiae orbis 
Lunae a terra erit 105,787. Et ponantur 20 milliaria pro 
dieta. Ergo si iste numerus dividatur per 20 exibit numerus 
dietarum 5,289, et restant 7 milliaria. Et si istae dietae divi- 
dantur per 365 dies unius anni, exibunt anni 14, et restant 
dietae 1 79, quae si dividantur per 30 quae sunt dies mensis 



MATHEMATICAE IN DIVINIS UTIUTAS. 229 

perfecti, exibunt menses pcrfecti 7, et restat unus mensis im- 
perfectus, id est, 29 dierum. Patet igitur quod sumendo 
dietam in %o milliaribus posset homo pertransire spatium 
usque ad orbem Lunae in 14 annis et quinque mensibus 
perfectis et uno mense imperfecto, et adhuc restarent 7 "lil" 
liaria et medietas milliarii, quae a principio relicta fuit. 

De nono vero coelo et decimo nihil potest per instrumenta Height of 
sensibilia sciri in altitudine et spissitudine et magnitudine, sicut *^^®°^*- 
de aliis coelis, ut de spissitudine octavi coeli quia haec omnia 
latqnt sensum, et ideo super haec cessat certificatio quantitatum 
et altitudinum, et spissitudinum. £t per longitudinem pro- 
pinquiorem Lunae est manifesta longitudo longior orbis ignis, 
sed longitudo longior aeris non est nota. Nam philosopbi 
haec neglexerunt, quia non est utilitatis notabilis. Quantum 
tamen est usque ad locum nubium verificaverunt, quoniam 
demonstratur in libro de Crepusculis^ quod altitudo illa est 
per 51 milliaria et duas tertias. Plinius' autem secundo 
Naturalium recitat nubes elevari stadiis 400 et 900 secundum 
diversa philosophorum testimonia. Ergo ad minus extenditur 
aer in tantum et plus; quamvis Albumazar et quidam alii 
aestimant vapores non elevari nisi per duo milliaria et decimam 
et tertiam milliarii. £t Ptolemaeus in libro de Dispositione 
Sphaerae dicit, quod decem stadiis est ultima elevatio vaporum. 
£t Martianus in Astronomia in hoc concordat. Nam montem 
altissimum ponunt decem stadiis elevari, ut Olympum, in 

' This book is generally attributed to Alhazen, and, like the treatise on Optics 
of the same author, was translated into Latin from Arabic by Gerard of Cremona. 
It is an attempt to determine with geometrical precision (a) the position of the 
Sun with reference to the horiion when evening twilight ceases or morning 
twilight begins : {b) assuming twilight to be caused by solar rays passing through 
terrestrial vapours, the height above the Earth to which these vapours rise. 
He found that at the extreme limit of twilight the Sun was between nineteen 
and twenly degrees below the horizon. From this datum, and from the thrce 
data of